The company is free to stop offering new copies of their software under a particular license. Whether they can retroactively revoke a license already granted to someone is a very different question.
The GPLv3 is explicitly irrevocable, so if the software was licensed under the GPLv3 (or GPLv2-or-later), the company cannot revoke any of their old licenses. Under the GPLv2, the situation is more complex and jurisdiction-specific, but the answer on Are licenses irrevocable by default? has some helpful guidance: in the United States, a license can only be revoked if there was no "economic consideration" exchanged for the license grant. However, "economic consideration" is much broader than mere payment; it can also include, e.g., economic benefit from publicity gained by offering a free-of-charge FOSS product. In that sense, you may have already granted an economic benefit to the licensor when you downloaded the software, diminishing the licensor's ability to revoke the license.
However, even if neither of the above condition apply (explicitly irrevocable license or economic consideration) and the license is revocable, this would only impede your ability to further share the software and prepare derivative works. Your ability to use software you have obtained is not something copyright law can deny you (at least in the U.S.), similar to how copyright law cannot disallow you from reading a book. (Contract agreements might place limits on how you can use the software, but you never agreed to any contract with this company; they freely offered you the GPL'd software with no terms on how you may or may not run it.)