Mail and Exchange can be a bit iffy, but this is usually a problem with the Exchange server. Mail on the Mac uses a different method of communicating with the Exchange server (Exchange Web Services) than do iOS devices (which use ActiveSync), so your Exchange server may be having problems with EWS. I'd suggest you first discuss this with the support resources for your email provider before you spend a lot of time spinning your wheels trying to sort things out on your end.
As a quick test, you can try this Microsoft tool:
and see what it reports re. EWS connectivity to your server.