Question: I am using a product whose code is covered by GPL2. All fine except that when a major update is released, it relies on database changes which are effected by a script (sometimes hundreds of lines long) which is not included in the GitHub repository. The authors are only willing to provide this script to those who subscribe to their extended support/partnership package. Are they entitled to apply this restriction?

Answer: 
That's fine.

You receive the binary and the code under GPL. So you have the source code for the software you use and are allowed to make whatever modifications you desire. The license does not make any comment on updates whatsoever; in particular there is no reference that you are entitled for easy upgrades from one version to the next.

A script to faciliate upgrade from one version to another, working on a database, is in principle just an external tool to allow you to upgrade your data structure for digestion from one version of your software to another. It's nothing special. It could also just be a migration script from one software to another completely unrelated.

Writing such migration tool only needs knowledge of the public API for the database - so it's usually fine to consider it not a derivative of the code.

Yet, even if that were not true, one would have to look at the copyright ownership: If the company or person releasing the programme is the sole copyright holder, they are not bound by the license themselves and can choose to release any part under whatever license they choose (or not at all). If they are not - the previous paragraphs apply.
The approach you describe in your question very much looks like the ['freemium' business case](https://en.wikipedia.org/wiki/Freemium). You get something for free, but if you want to use all features (in your case: migration of data from one version to the next) you need to pay a fee.

This business model is usually OK, and if it is the case (an assumption, you seem to indicate this) that the authors of the free database and of the script are the same individuals (copyright holders), then there is not even the question about code overlaps.

So yes, the authors are OK to do this, I cannot see any GPL violation.