There are several of us in the same boat getting the same 503 error. This thread might help you out: Plex Crashes Frequently: 503 Service Unavailable
I think my issue might be a connection to a friend’s server that is no longer active creating so many requests (4097 to be exact) that the server crashes. I deleted that connection and so far so good – but it’s only been a few hours.
Although now my DVR has disappeared, which is another issue the latest PMS build is causing folks. Plex used to be rock solid, now with all the bugs it’s more like whack a mole …