In Plex for Android 5.10.0.160-beta (and the previous beta as well) chromecast playback is paused when I turn off the screen, go to home screen or simply back out of the “playing screen”. I’ve never seen this behaviour before.
Device: Nexus 6P (O - developer preview 2)
Same problem for me.
I am having this problem too with the same update version @jens.bergqvist mentioned.
I can workaround it, when the focus is taken off of Plex, pull down your notifications and resume playing from the Chromecast status.
Device: Samsung Galaxy S8 SM-G950U (T-Mobile)
Android N 7.0
Samsung Experience Version 8.1
I am also having this same issue. The same workaround given by @nibble4bits worked in my situation as well.
This issue appears to be solved in the latest beta (5.10.0.232).