It seems I have got the same problem as described here. The symptom is that the Exchange sync never seems to finish. The phone runs hot, drains the battery, and (probably) uses a lot of network traffic. The problem is that the disable/enable of Calendar sync trick fails on my iPhone. It tries for a long time and then it times out. I can't even remove the accounts completely, that fails in the same way.
It's an iPhone 5S running iOS 7.0.5. I'm syncing three calendars. Two Exchange accounts from different servers and one Gmail.
This problem happened to me once before and then I ended up doing a Factory Reset. I'd rather not do that again.
Power assertion timeout:https://dl.dropboxusercontent.com/u/26840/iOS_power_assertion_timeout_DataAccess_Exchange_related.png and with https://dl.dropboxusercontent.com/u/26840/iOS_power_assertion_timeout_fetchMobileSynchronously.png
The preferences timeout: https://dl.dropboxusercontent.com/u/26840/iOS_preferences_timeout_turning_off_calendar_sync.png
I would love to find a solution to this! It could be to the root of the problem, how to force calendar sync off, how to force removal of email accounts, or to something that I've missed.