So you thought you might catch why a T-1 router is failing by being clever and sys-logging you find that this only confuses the matter by telling you that serial interface went up during one of the outages (i.e. no corresponding down event!)......
Make sure the gear is not plugged in to a failing UPS unit! Power cycle the unit to simulate if you want to prove it to yourself and you will find the same events in your syslog!