I would like to include a figure from a scientific paper which illustrates some background for my invention. I can cite the source and I can make it clear that I'm using it for illustration and discussion purposes only.
Is that a strong case for "fair use" or do I need to be concerned about violating the original author's copyright?
I will only address the legal question asked, about a fair use defense of such copying. I presume that the copyright holder has refused permission to use the figure for free (or perhaps at all), or else the right-holder is uncontactable. If the former, you have a good estimate of the chances of getting sued.
Fair use is determined via a balancing act involving purpose, nature, amount and effect. Purpose ranges from commercial exploitation (on the "not" side) to non-commercial education. Patents exist "to promote the progress of science and useful arts", which is more in line with educational use. W.r.t. "purpose", the uses is more in line with fair use than not (compare that to "make a tee-shirt from it and sell a zillion copies", not fair use). Nature has to do with "what kind of work was the original -- factual versus creative?", and here because this is a scientific paper and you are apparently reporting facts in some form (not copying a Chagall painting), the proposed use favors fair use. Amount refers to the gravitas of the copied part relative to the whole. In a typical scientific paper, a figure is just a summary of certain facts which, while important for the paper, is not the essence of the entire paper. The typical standard for copying a figure adopted by major publishers is that a figure can be copied, and two figures requires permission (their reasoning is informed by prior lawsuits, and is not itself a form of law). Finally, effect regards what market harm your copying did to the copyright holder. It is highly unlikely that the publisher (let's call them Alsavior) will lose millions of dollars from journal subscriptions and access fees because you included a figure from one of their journal articles. It is likely that the effect on market will be near zero. Then there is the fifth factor, "transformativeness", which asks whether you are just copying, or are you creating something entirely new in the course of copying the original – this isn't a "just plain copying" use. So all told, a fair use analysis looks promising.
At the same time, because there are no bright lines and it is a subjective balancing act, one is advised to either avoid the problem entirely (paraphrase, do not copy), or hire a lawyer, or both.
Contrary to what is stated in another answer, the text and drawings of patents can be copyright in the U.S. From the Compendium of U.S. Copyright Office Practices:
Patents, Patent Applications, and Non-Patent Literature The U.S. Copyright Office may register a claim to copyright in the written description for an invention or the drawings or photographs set forth in a patent or a patent application, provided that the work contains a sufficient amount of original authorship.
The patent office requires that you allow reproduction of your patent and patent application but you can conceivably stop people from other uses of text and drawings in your application.
Also contrary to another answer patent applications are published by the USPTO. So the question comes down to the drawing you are planning to reproduce. Presumably you can convey the scientific/technical content the drawing contains in a drawing, data table or other means of expression.
Note that another answer states that you are required "provide prior art and the demonstrate how you are novel relative to all prior art." That is not correct. You do need to make the patent office aware of relevant prior art. This is usually done by citing documents on an Information Disclosure Statement. It is not your job to show that your claims are novel - it is only your job to counter the novelty arguments the examiner cites in an office action.
First, the patent application process is not subject to copyright law restrictions1, fair-use applies liberally — and while some portions of a patent (mask work, a drawing, or a photograph) may fall under copyright protection (to make a clear example, placing a photo into a patent does not in itself make that photo public domain), the USPTO states:
"Patents are published as part of the terms of granting the patent to the inventor. Subject to limited exceptions reflected in 37 CFR 1.71(d) & (e) and 1.84(s), the text and drawings of a patent are typically not subject to copyright restrictions."
Patents are also not "commercial" in nature (by commercial I mean such as an ad in a magazine), and they are not "commercial publications," these are factors in determining fair use.2
Research papers, are of course protectable under copyright law, but are also subject to fair use limitations.
FAIR USE: Pursuant to 17 U.S. Code § 107, certain uses of copyrighted material "for purposes such as criticism, comment, news reporting, teaching (including multiple copies for classroom use), scholarship, or research, is not an infringement of copyright."
These things being said, a patent isn't a "commercial" use such as a use in a published article that you wrote for a journal - if you were going to write an article and cite the author you would almost certainly need to get permission to reprint a figure, as that is a commercial, published re-use.
If you are citing the author in a masters thesis on the other hand, that could use the figure under the "academic use/research" umbrella of fair use, which is permissible. (But permission would need to be sought if that thesis were to be later publishied).
There are a few unique aspects of patents, one of which is that you are required by law to list relevant prior art relating to your patent. The examiner will also add further prior art to your patent in the course of their examination. Prior art is either other patents or relevant research papers and studies.
Does this figure support your patent claims? The only thing in your patent that is "actually" important are the claims. The claims are what defines your legal "rights" and what must be "novel" in view of the prior art. The claims are the only part that gives you a right or cause to sue.
As such, the rest of your patent application is there simply to support the claims, by making the invention very clear, and providing the context of the prior art.
If this figure is required to present prior art, then that would clearly be fair use as you are legally required to provide prior art (and then demonstrate how your invention is novel relative to any prior art the examiner bases an objection or rejection of a claim of your invention.)3 The USPTO has sided with the defendants in such cases, noted below:
There is case law supporting the fair use of published material in patents and patent applications.
This article is a good summary of recent cases. And This Article discusses more of the relevant case law relating to this subject.
Side note: since you are asking the question I assume you are filing pro se? Which book are you using? My friend Richard Goldstein wrote this book on obtaining a patent, which I recommend. He was quite helpful to me on my patents. Also, I've used the Nolo book by David Pressman "Patent It Yourself" which I also recommend.
Due to confusion over some areas of this post, here are notes to clarify:
This is not to say that limited aspects of patent document can't be protected by copyright, such as a photograph, though the practice is rare. My original comment comes directly from Patent Attorney David Pressman who states:
"If you see any prior-art patent whose specifications contains words, descriptions, and/or drawing that you can use in your application, feel free to plagiarize. Patents are not covered by copyright and it's considered perfectly legal and ethical to make use of them." (ISBN 0-87337-563-7) 2001
a. Though due to the controversy of the initial post, on which I relied on this statement, I looked deeper and I see Pressman, Esq. adjusted his statement for the more recent edition:
"...unless a patent states that it is covered by copyright, the PTO does not consider that patents are covered by copyright..."
b. Moreover, while Mr. White stated "...conceivably stop people from other uses of text and drawings..." I have been unable to find case law that directly supports this, though there is Rozenblat v. Sandia Corp. Where patent holder Rozenblat sued claiming copyright infringement on his patent. He lost, though the court indicated that copyright could apply in some circumstances. 
Just to be perfectly clear, I never stated in any way that patents are not published. Of course they are. Nevertheless, the PTO Official Gazette is not a "commercial publication." When the USPTO publishes a patent, it is wholly different than a commercial publication such as Scientific American publishing a paper. This should be self-evident, but apparently was misunderstood.
I re-worded and expanded this sentence to clarify. Nevertheless, It should have been obvious in the original short form that it was a general discussion of the foundations for claims.
a. No where in my post do I speak exclusively of the original patent application. The wording and terminology used in the original and updated posts is intentionally generalized and related to the overall process and general concerns of obtaining a patent.
b. Section 1.111 (c) states in part: "...the applicant or patent owner must clearly point out the patentable novelty which he or she thinks the claims present in view of the state of the art disclosed by the references cited or the objections made. The applicant or patent owner must also show how the amendments avoid such references or objections."
Best Regards, and thank you for reading.
