@benjaminwolf thanks for the logfile!
There has been some improvements with the PMS connection handling in next release, should be ready in a few days, but I do not think it will affect the issue I can see in your logfile.
It is also possible that 0.7.1 shipped with a bad kernel and raspberry pi firmware, next release will ship with linux kernel 4.1.10 and latest rpi firmware.
From the log I can see that PHT might have mixed up the plex.tv service with the cloud sync server and it fails to load playlists from the cloud sync server at the wrong path, this is very strange and nothing I have seen before.
It also looks like PHT is trying to reach your PMS using http connection and fails every 30s or so when you resumed playback, unclear why it retries to connect over http when it has a https connection.
Please try to disable cloud sync servers in RasPlex and change your secure connection setting from required to preferred in PMS and report back if this solves your problem.