yes, I don’t think it is a matter of concurrent connections, but rather leased to machines with a time to live. For example, your licence might allow for 10 users. Number could be anything. You have 12 machines. Even though you log on one at a time, each one is given a time to live. A lease period, when a machine/account does not re authenticate within a set period of time, it expires. Meaning that machines/accounts take its place in the queue, and later you will find the system that lost it place might not be able to log on if other machines have been continuing to use the network.
You mentioned that some machines that could not log on now can. Im betting if this has happened, then one of the original machines might now have lost its lease. And therefore it is issues on to a new system. I had a very similar issue with a soho unit many years ago. It was killing me. part of the product. But this is only one suggestion. If you think its a configuration issue, you can always image a working system onto the one not working. and check if that works. otherwise I cant see why the router will allow one to get through and others not.
but then to do your head in. GRE generally related to your error because of a block.... but you still have access with others. can you image the machine with an impression of a working system? Ghost, shadow protect etc... just do a search for some freeware. im sure something will be listed. unless you have data you cant loose. then I would suggest swaping the drive to test it. sorry for the essay. but can imagine your frustration by now.