Hi there,
This is a most curious issue indeed, and I suspect has to do with an outdated network driver, or something of that sort. When AI War starts up a single player game, it does indeed fire up the network port as a host server (since it does not particularly differentiate between SP and MP), but it doesn't actually send any data out through it. So, there should be no reason it would interfere with your Internet connection, especially not after so long a period as an hour (if it was to do anything, based on how it works, I'd expect it to happen immediately on loading a game -- not that I'd expect it then, either).
It's a bit mysterious, not something I've ever heard before, but I'd suggest upgrading your network drivers as the most likely solution. Perhaps this is some sort of low-RAM issue if AI War is using a high enough percentage of your RAM that your network driver is flipping out or something; that's the only thing I can think of, and would be something hopefully fixed by a network driver upgrade. Hope that helps!