The same or similar problem is very common. It's very likely to be down to corruption on the hard drive which might be fixable by triggering a GSOD using the kickstart codes. Do you see a flash of green before it reboots or does it just go black?
It can also occasionally be a symptom of a failed power supply - I've seen this a few times and the TiVo just reboots when it would normally go into the startup (man on slide) animation.
It can also occasionally be a symptom of a failed power supply - I've seen this a few times and the TiVo just reboots when it would normally go into the startup (man on slide) animation.