It appears that ObjectAid LLC has gone out of business. Their website has gone offline, and the DNS name "objectaid.com" is currently "parked" at GoDaddy.
(For people who want to find the old website, check here.)
However:
We don't know that they have gone out of business. Someone might have simply forgotten to pay the bill for their DNS entries.
Even if they have gone out of business, someone still owns the IP rights for the software that ObjectAid LLC has developed, and someone probably still owns ObjectAid LLC's rights in any contracts with their users.
The "someone" might be the original owners of the company, the company's creditors, or some other company that is taking them over / buying them out. Those people may still have ideas of monetizing the remaining assets.
If you were to attempt to develop a work-around for their license management system being off-line, that would probably entail reverse engineering the software, which is probably a violation of the terms of your license with ObjectAid LLC. That may place you at legal risk.
If you ... or someone else were to publish details of a work-around, that could be illegal depending on where you are.
Just using such an work-around could be illegal, depending on where you are.
If Stack Overflow were to (knowingly) publish an Answer containing a work-around, then Stack Exchange would potentially be liable for damages. And since they most likely have "deeper pockets" than you do, Stack Exchange would likely be the primary target for (hypothetical) lawsuits aimed at getting a payout.
None of the above should be read as legal advice. If you feel you need something more definitive: 1) read the fine print of your license, and 2) talk to a professional lawyer.
My advice would be: don't develop a work-around. And if you do develop one, or find one, don't share the details here.
Instead, start looking for an alternative to this plugin.
For the record: 1) I don't know of a work-around, and 2) I don't know of an alternative.