Hi,
I had the same problem and it was a real pain. I tried EVERYTHING and nothing helped. I deleted the account (several times), cleared the cache, wiped out calender entrys on the server that was recurrent, tried to set the sync to only sync mail, for one day only and lastly factory reseted the phone. Nothing worked.
Finally, and what did it, was to set everything to push, all the time. No manual schedule or "every 15 minutes" at all, just push all the time. This did it, believe it or not. Now I can't even see the Exchange Services in the battery stat any more. I am enjoying a healthy battery that have plenty of power left at the end of the day, although I still receive around 40-80 mails a day and it's pushing them all. I have sync for calendar, mail and contacs and I sync all mails and the whole calendar.
For me, with a Samsung GS3, this solved all the issues instantly. I had to set the notifications off, but that was worth it for me.
I think the source of the problem is on the server side, as it all started when we moved to Exchange 2010 server. On the other hand, a colleague that owns a HTC One does not have any issues, regardless of the settings he is using. Maybe HTC has their own solution to the exchange sync, I have no idea. As for my Samsung GS3, the problems are all gone.
Worth a try maybe?