Went back and forth a bit with jstefanop for a bit to figure out why my Apollo II could sync & solo mine, but wouldn't stay connected to a pool. Wanted to share what we found in case others encounter the same issue:

Asus routers (and presumably others) have a feature called AiProtection with a a Two Way Intrusion Protection setting that will specifically block bitcoin mining.

https://www.asus.com/support/faq/1008719/#a3

You'll have to disable this if you plan on mining behind any router with a similar protection. Worth noting that it can sometimes be automatically re-enabled during a firmware update.