It's been a long time but I wanted to update this incase anyone else runs into the same issue.

I continued to have problems with incoming calls. Most commonly, the phone would ring. When I'd pick up, all I'd hear is dead air. The caller was usually sent to voicemail. I'd then be unable to place a call or get a dial tone for about 30 seconds. Support just kept telling me to check my port forwarding settings and making mysterious config changes on their end.

The odd delay got me to thinking - what if the ATA was crashing and rebooting? Sure enough, the next time this happened, I logged into the HT502, and it showed an uptime of just a minute. Confirmed that the uptime was always reset after one of these events. I reported this to support. They tried updating the HT502 to the latest firmware, but it didn't change the behavior. I found a post from someone else using the same ATA on PhonePower that had the same symptoms (he actually had two HT502s, one exhibited this issue the other didn't).

VOIPo sent me a new ATA. Bingo - uptime is over a week, and I've actually been able to speak with each incoming caller. Finally!