Hi,
I've noticed a lot lately that if I am trying to sync a largish movie, say 10GB, to my iPhone, more often than not it will fail to copy - it seems to relate to if the iPhone screen locks itself after it not being touched for a while (based on whatever autolock settings you have enabled I guess), as I think WiFi disables at that point. I seem to be able to improve it if I leave Plex on the Sync screen, and have the iPhone plugged in, it might be the workaround.
Anyway, the main issue is not what the iPhone does, but that if the sync copy is disrupted for any reason, when it next does a Plex sync it deletes the file it was copying and starts again from the start; please replace the basic copy mechanism with a resumable copy to save effort.