Hello folks. I wanted to try to help with Apple Mail. I may have a resolution. Below I (1) explain the issue; (2) offer background; and (3) describe how I took care of it with help from Apple Support.
Here is the issue. I started to get the spinning beach ball. I would force quite Mail, relaunch, and it took maybe 10 tries and it would run okay for about 5 minutes before freezing again. This happened for a full day.
Here is the background. There are two facts that may or may not be relevant: (a) I was one of the 1.1% who lost Apple mail access for 48 hours back in September 2012; and (b) I just upgraded to the most recent version of Mountain Lion when this problem arose. Additional background. I have a .mac account, a gmail account, and three Exchange accounts associated with my job.
Here is how I took care of it. I tried everything.
Force Quite
Rebooting
Reinstalling Mountain Lion
Deleting Mail preferences
Deleting all preferences
Rebuilding mailboxes (when the program was running for a moment)
Eliminating bundles/add-ons such as Mail Act-On and Spam Sieve
Safe Boot
I also tried a guest account on the same machine. Same problem. But my iOS devices worked fine. And Apple Mail worked fine via the web.
Apple Support walked me through all sorts of options, mostly what I tried above. The support guy -- I was passed to the advanced guy -- was actually complimentary, because I listed everything I did, and he said that was all eh would have recommended.
He did give me the top that led to the solution. I am not sure why. But in System Preferences, under Mail, Contacts, Calendars, I turned off all five accounts. Then I turned them on one by one. It seemed as if the Exchange accounts were the problem. With the .mac account enabled, but not the others, Mail launched and I had the spinning beach ball for about 30 seconds, then it worked fine.
However, after I got it working, and I was thinking I'd call IT at work, I tried again, enabling the other accounts (from inside Mail), and it worked fine.
I'm thinking unchecking all accounts from System Preferences. then re-enabling, did the trick. But everything else probably helped as well.
For what it's worth.