This seems to happen consistently, and it's pretty unnerving. If I pause a video, then after some time Plex will automatically resume playing. It will happen while I'm in a different room, say; definitely not touching the remote.
I haven't timed it, but it seems a bit random, which I can infer from the fact that my speaker system automatically turns itself off after a period of silence. Sometimes the video resumes while the speakers are still on, sometimes not.
I don't know if this is caused by Plex's video player or Apple's.