To troubleshoot and see if this is indeed the issue, you can check all mDNS records on your network using zeroconfServiceBrowser | Tobias Erichsen (tobias-erichsen.de).
I would run it when everything works as expected (you should see an entry for your P1 dongle) and save a screenshot of it and then run it again when it fails and compare.
If this is indeed the issue, then depending on your network device, configuration and troubleshooting will be different. Sometimes, mDNS is also overloaded if you have too many devices using it. You can get more info here on a potential solution: Issue with Google Chromecast
