After seeing a number of posts from people who are seeing this behavior, I decided to test for it on my phone. I rebooted my phone and immediately enabled airplane mode. I then attached some earphones, set Poweramp to shuffle play and set the phone aside. That was almost 6 hours ago. It's still playing music with no messages about missing licenses.
For what it's worth, I'm running a Nexus 6P with stock 7.1.2. Poweramp 2.0.10-build 588-play (Full version)