Could be a bad cable going into the T1 hardware, or something bad with the T1 hardware itself. It could also be something wrong on the other side of the T1 and it's refusing packet delivery while it retrains. I'd get your T1 supplier involved - most T1 hardware has troubleshooting tools built in to help track this down - give your provider the exact time of the problem and see what the T1 hardware logs have to say about the problem. If there is not issue visible there, it may be in the T1 device on your "edge" of it, like a bad solder connection or similar. Most providers are going to be pretty helpful with this type of thing and they'll probably drop new hardware in there.
I'm totally shooting from the hip here - I don't know anything about your hardware and only have a single failure point to go from - so forgive me if I'm barking up the wrong tree. The squirrel may be elsewhere, but the leaves are shaking on *this* tree.