Apple's power adapter may have a self-resetting circuit breaker which would explain the reason it resets itself. What causes it to trip could be an overcurrent condition caused by a number of factors. Excessive heat may be among them.
The APC 350 is a fine UPS, but bear in mind that it is not running off its batteries constantly. It will switch very quickly in the event power is interrupted, and provides adequate surge protection, but can do nothing to protect against phenomena such as harmonics that could explain your premature and frequent power adapter failures.
Obviously Apple will honor their warranty but you may benefit from power conditioning provided by a so-called "true online" UPS. They are expensive and overkill for most people but given your circumstances I'd at least familiarize yourself with what they do.
You may also want to determine if your residential power is a causal factor. I think a competent electrican with the appropriate measurement equipment ought to be able to advise you on that possibility at a reasonable cost. If something is wrong you may have more expensive equipment at risk than an $80 power adapter.
Power quality was never a concern when the typical residential loads were lights and motors, and home electronics used robust linear power supplies with iron transformers. Everything was a purely resistive load. Just about everything you buy today is far more complicated and delicate, and it's not just computers, printers, TVs, and home theater equipment... it's refrigerators, air conditioners, toasters, and CFLs. Even magnetic ballasts for fluorescent lights have been discontinued in favor of delicate electronic ones that don't last. Add regulatory demands for energy efficiency, and the result is millions of homes filled with nonlinear loads that never existed before.
The problem is not getting any better, and you may just be on the leading edge of it 😉
