Originally Posted by Mussels
i'd say test without the UPS - sounds like you could be overloading it.
I did that and it's been running for several days now, problem-free. This UPS has been a little twitchy for the last several months. It's a 350VA unit which worked well for all my other (less powerful) setups, but it looks like my current build has taxed it far beyond its capacity, and the system reacts badly if there are any power interruptions. It probably needs a new battery, but if I'm going to spend $30-40 on one of those, I may as well upgrade the whole unit.
Thanks to all for responses and advice.