If you computer is set for automatic updates you might want to check what time it updates itself or any other programs that run an auto update. The network congestion might be enough to make you time out and d/c.
If that is not the case you might want to check with the phone company to see what time they test the system. Everynight one of my telephones give a slight ring at 11:03 p.m. (just as I'm going to sleep of course :? ). This used to make my TiVo stop updating during the night.