The rigs themselves are still connected to the internet, and are accessed remotely via logmein each time this issue occurs. I've only been able to resolve the issue by switching pools thus far. Temps are in the mid 70s for all affected cards, so I'm assuming that isn't an issue. What the heck is my problem?
It's usually not a problem on your end, but the pool's.
Do you have lots of connections going to the same pool?
I had about 12 miners all pointing to the same pool once and 2 of them always had this same issue, after I split them among 2 pools problem went away.