I too am having this problem. I updated to 8.1 on my iPhone 5 when the problem started. If I reboot the phone, mail to Exchange (Office 365) will work for a while and then stop working. I have tried the suggestions of changing the amount of days to sync (currently set to three days) and still not working. I tried re-entering my password for my Office 365 on my phone and I also went in and cleared out any old entries of Phones in the Exchange settings on the web site.
It appears to be a 8.1 issue as that's when I started seeing this problem. Again, rebooting the phone makes mail work for a while, but then it will stop and only spin when getting messages. Access to my iCloud email account still works and it is only Exchange email access.
I have not seen this same behavior on my iPad. I just updated the iPad to 8.1 yesterday. Mail is still coming in on the iPad and not having this same problem. However, I did notice that on my iPad I have a message from September that I deleted long ago that will not delete. It only shows up on the iPad though.
Odd things happening with Exchange email access for iOS 8.1.