The cost of filing a copyright for an updated filing would generally be the same as the original one. The amount of work isn't much different and there are good reasons why every new version of software sold on a large volume commercial basis should always have a new copyright registration for a new version of the software, which are essentially the same reasons you copyright the original version of the software in the first place. As noted by @DavidSiegel in a comment:
A work is protected the moment it is "fixed in tangible form", but one
cannot sue for infringement unless the work is already registered
under 17 USC 411. Statutory damages, often important, are not
available unless the work is registered before the infringement
occurs, or within 3 months of publication, under 17 USC 412.
$2,000 is on the high side for the work in the Colorado market where I do most of my work, but it isn't unheard of or terribly beyond the norm. I can think of at least five plausible and defensible reasons for a fairly high charge for a fairly simple job.
This said, sometimes people just charge more than the going rate for work for no good reason, and in a free market, people are allowed to do that, at the risk that someone will go to the competition instead at some point.
One reason: value billing
Many lawyers do that kind of work on a flat fee basis, spreading the significant costs they incur in putting together an efficient system over many cases. They can do the work efficiently but want to charge a rate competitive only with lawyers who aren't so efficient and have to figure things out from scratch each time.
A second possible reasons: diseconomies of scale
Part of what may be going on is that if you have a big bureaucratic law firm, there are significant firm wide costs to every new matter (which, for example, has to be cleared through a conflict check firm-wide and involves quite a few administrative set up costs), especially if the firm charges high hourly rates.
In firms with those kinds of economics, even a project that only takes two hours at $400+ per attorney hour to do the core legal work, would be hard for the firm to make a profit on, because there might easily be $1,200 in anticipated setup and shut down, and tail case monitoring costs.
While some of those costs could, in theory, be streamlined when doing repeat work like the job suggested in the question, large or high cost bureaucratic firms aren't necessarily bothered to provide discounts in those circumstances to repeat customers because they see that kind of job as nickel and dime work that distracts them from working on their core competency of high-end big litigation cases, and big transactions like mergers of medium and large sized companies.
It would probably be possible for a small, more nimble firm that doesn't see this kind of job as a distraction to get the fee for this down to $500-$1000.
This cost issue with small transactional matters is one of the reasons that it is quite common to see the intellectual property department of large firms break off from the large firm bureaucracy (I recall it taking immense efforts just to requisition new office supplies when I worked in one because there was so much red tape involved), to form vastly smaller "boutique" intellectual property speciality law firms (e.g. 5-25 lawyers breaking off from a 100-500+ lawyer law firm) to prevent that kind of cost creep for smaller matters. The economics of high end intellectual property transactional work is different than a lot of big law firm work because a lot of intellectual property transactional work is high volume, low dollar transactions for repeat clients, which makes the friction associated with big law firm bureaucracies outweigh their benefits.
A third possible reason: price for this job doesn't matter much in the context of a larger attorney-client relationship
On the other hand, if you have a big company that normally uses a big inefficient law firm for its work (since most of its legal work involves life or death of the company grade issues where winning is much more important than keeping legal fees to a minimum), and it has a low volume of intellectual property filings, it may be more efficient for that big company to simply pay a bit more than it could if it really tries to get its costs down to a bare minimum, to just continue to use its regular law firm for this bit of work.
The cost of vetting an alternative law firm may not be worth it for a big company. Bidding out the small project might save a few thousand dollars a year of legal fees, but if the big company normally has hundreds of thousands of dollars a year of legal fees anyway, this may not be a big deal for that big company client.
A fourth possible reason: a bigger ability to make malpractice right
Also, keep in mind that if the software has very high economic value, a big part of your $2000 flat legal fee for the work may be paying for the malpractice policy to make the client whole in the unlikely but inevitable event for a screwed up filing that has high stakes to the client in the rare cases where it happens.
For example, I recall a malpractice case my office once handled where a big firm failed to file a key document in the real estate records resulting in a $20 million dollar mortgage losing its priority when the borrower default on the loan made by the client due to a miscommunication between a junior lawyer and a paralegal over who was going to get that job done that resulted in neither person doing it. This resulted in an immense loss to the client (they only recovered about $2 million and would have recovered the full amount if this document had been filed on time as the law firm agreed it would). It doesn't happen often, but it happens.
In the same vein, if your software product generates $20 million a year in revenues and a small, lower charging firm screws up in a way that materially impairs the copyright protection available for that product (e.g. causing statutory damages to be unavailable when large statutory damages would otherwise almost surely have been awarded), a small law firm's malpractice policy and the responsible lawyer's assets may not even begin to cover the harm done, but a big law firm's malpractice policy, which is far more expensive and makes everything that the big law firm does much more expensive to clients, might easily be able to cover that loss.
A fifth possible reason: the lawyer is reluctant to do the work
An alternative explanation is that the lawyer could do the work, but isn't really bothered to do it unless its very lucrative, since the lawyer sees it as a distraction or just doesn't like you as a client.
If this is the reason, then the lawyer is setting a high charge to encourage you to go elsewhere, without saying anything that would cause you to lose face or that would damage the long term lawyer-client relationship in a future case that is bigger or more in the usual vein of the work that the lawyer is looking to do going forward.