Same here. Other threads regarding this issue:
https://forums.plex.tv/t/chromecast-has-to-restart-streaming-every-time-you-close-ipad
https://forums.plex.tv/t/plex-keep-disconnecting-chromecast-when-ios-is-idle-a-few-minutes
https://forums.plex.tv/t/chromecast-playback-suddenly-terminated-after-re-opening-ios-app
Hopefully a Plex developer will to look into this.
