I am also using HTC's EAS Sync system to connect to my Exchange server and encountered this same issue.
Battery pulls and resets did nothing.
Go into Settings > Sound & Display > Screen Timeout.
You see how there is something called "15 minutes (Exchange ActiveSync Policy)"? Well, even though mine wasn't checked (in fact, the 30 seconds was checked), it was defaulting to 15 minutes, after I installed a certain app (ColorNote).
So, I just checked 15 SECONDS, closed out, and it was fine. Later, I changed it back to 30 seconds. It has never happened again.