Random restarting happens under two conditions that I've seen - one power related (see the rest of this thread for ideas on how to solve power sensitivities), but the other is when the device is pointed to two instances of the same proxy if your network has any appreciable traffic.  When it gets "confused" it tries the other proxy, which is the same if you're not running two separate copies, so then it stays confused, stops processing work, and then the device does the auto-reboot when it notices it's been without work.

I solved this second type by running two separate proxies, and having it switch between the two.  This approach works for two mining_proxy (slush's proxy program) instances, but if you're using bfgminer, I've found the better solution is to have the second pool point to a port that is not active (but is on a real machine on your network - it could just be the same ip address but a different, unavailable port, say 8425 or some such), so it bounces after enough time to get unconfused (a mere hiccup), and then it gets back to hashing.