Here we are in early April. All has been well since Jan 6th. Can't say that I've used this system every day, but perhaps a few times a week, each week, since between then and now. I forget when I last used it, though it was certainly last Sunday, and I'm pretty sure at least once during this last week. So, today, I'm back to having A not connect, though S is fine and B is connecting fine. A is seeing the SQL Server(s) on S, fine, as well, it just refuses to connect, either through SSMS or the program.

So, the state of the matter is: This problem will go away for months at a time, but then will spontaneously come back. When it comes back, it can stick around for days, is immune to reboots, and pretty much anything I can think of doing, and then it will vanish as mysteriously as it arrived.

In general, I feel that it is probably a router issue, since the problem began when I got the new router. Also, there are times when I boot up A and it can't get to the internet at all. This time, it's kind of good timing, though. I'm about to leave for a week, so perhaps it can sort itself out in the meantime.

If anybody has any further suggestions on the topic, I'm open to them...but I won't be responding until I return.