I guess my first question is... what do you mean by "an APC"? Do you perhaps mean a UPS (possibly one manufactured by APC)? If so... to me, that sounds like a workaround (versus a solution) that might work as long as the outage doesn't exceed the UPS' capacity. Regardless... the computer geek within me would want to try to pursue a software solution before attempting a hardware solution.
Have you ever had physical access to the Pi after one of these outages? Is it really dead in the water, or is it at least running and perhaps only certain pieces of the hardware didn't come back up (Ethernet, for example)?
If it's running on some level, seems like it would be possible to utilize a service/daemon to perform a soft reset if you can somehow detect the error condition (e.g. have the thing check to see if it can reach the Internet every 120 seconds; if 2-3 consecutive failures occur, reboot it).