Insufficient power can cause instability issues, but you can try swapping the handset with another that works on the same LAN port, and see if the "good" one starts acting up and the "bad" one starts working ok to verify.
Note: It could also be the reboot that made the problem go away
@matthias check your POE switch supports power modes (classification/consumption modes) some switches will only supply power that is necessary to the power class (classification) where consumption will provide what is actually required from the phone.
I am assuming you have a managed switch of course.