My edited answer is addressing the "why is it constitutional part" of the question, with a foundation on how I came to the answer.
After further contemplation, it appears that the extension issue is more relevant in context to who the owner of the patent /copyright is.
A practical extension (which should be an exception) may be properly granted to an owner who got a concept to market late or due to another reasonable hardship. Then Extension should be granted, on a basis of "usefulness".
If it is a capital backed corp., just wanting to monopolize the market or extend royalties for some un-useful concept they took from a R&D agency or acquisition. Extension should be denied.
This application of law would be consistently "Necessary and Proper" to promote "useful" Arts and Sciences. And like other personal rights, it should be non-transferable except to heirs, to protect the creator from fraud and exploitation (but that's another matter unto itself).
Indeed the constitutionality operating on copy-rights is found under the treatment of Patent rights.
The invention of a font-style falls under a patent-right, the special use of the font-style to pen a novel falls under a copy-right. That is the end of the legal treatment of the personal ownership of a unique creation.
Regardless if it is a material design or concept to be used by industries or non-material idea or concept to be enjoyed by the senses.
They both involve the issue of the protected right to trade and profit from ideas (intellectual property) created in the mind. And also the reason they are put in the same constitutional clause.
A patent (right) and the right to copy and sell are the same principles. That have to do with personal (private) rights to property created by the author.
A Patent is a document [Title (property)] issued by the government that certifies exclusive ownership of an idea created and recorded on paper. And that includes exclusive *copyrights -- the right to copy, distribute, sell and profit from anything produced with a "likeness" of the intellectual idea contained on the registered deed. Google Letters of Patent.
And because corporations have no power to author or invent (create) ANYTHING as only man and Nature does. Extension of the time limits to corporate entities who may have sponsored or purchased the creation, would in principle be an Anti-Trust / Illegal Monopoly matter in-fact.
[The Congress shall have Power] To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries
A copyright is term and right to a registered patent of anything that was created / authored by use of Art and Science [knowledge] including the intellectual ideas recorded on any medium (drafts, schematics, music, and other writings).
For instance, a patent for a "formula" for a drug (Prozac, Viagra, etc), is no different than John Pemberton’s secret "recipe" for Coca Cola, if they would have actually registered the modified [sans cocaine coca-leaf] formula with congress to protect it only for a "limited time".
The fact of the matter is, that once you publish (distribute) something with the intent of making it available to everyone. It's no longer private property. And the use of Patent-rights or Copy-Rights is because you need the protection of our National government to allow you an exclusive limited time-frame to monetize your unique ideas and designs. After such 20 year time expires, it falls under fair use and public domain. (see the law on monopolies and anti-trust)
Here is some background from the Coca Cola example to clarify the relation of patents to other copyrighted information.
A patent is a “limited [copy]right granted by the government to an inventor.” Thus, for the duration of that patent’s life, which is 20 years, the inventor has the sole right to sell, make, distribute, and license that product. However, after that patent’s time has run, the formula becomes available to the public. In 1893, Coca-Cola patented its original formula, but after the formula changed, it was not patented again. ...A trade secret is a “piece of information whose value derives from it not being widely known.” ... While trade secrets are extremely valuable and generate a lot of publicity, there is virtually no legal protection if they are discovered unless the trade secret is misappropriated...