Sometimes they break
I've had this problem for the past month, and I finally figured it out....no thanks to HTC, AT&T or my Exchange Active Sync provider. They all told me it was their problem, but another provider's issue. I was about to throw them all under the bus.
My problem was that the Exchange ActiveSync calendar stopped syncing, although the email and contacts worked fine. Appointments from my phone would sync to Outlook, but any appointment I put in Outlook would not sync to my phone.
This is my solution:
On my HTC Vivid, android version ICE, 4.0.3, AT&T cellular provider.
I went to: Home, Menu, Settings, Apps, All Apps, Calendar Storage.
Clear Data in Calendar Storage. This should erase the Exchange Calendar from your phone. I did not even have the Exchange Calendar as an option to view when I opened my Calendar.
Now, Remove the Exchange Account, and re-install it. No need to turn the phone off in between. My calendar worked perfectly after that.
If you really want to be thorough, clear the data on the Calendar and Calendar Widget, also.
I could not clear the cache in Calendar Storage, Calendar or Calendar Widget - it was not an available option for me.
I hope this helps!!!