I had the same issue and looking over the logs, it seemed that there were corrupt emails which resulted in an endless loop of checking/downloading mail. We were under the process of migrating our accounts to a different server.
Our email accounts were using a SmarterMail server. I'm not sure if that was the culprit as I checked with the datacenter and was told that no other users were experiencing this. We migrated our mail to Rackspace and everything has been working fine ever since.
There may be, however, something that could be tried (I didn't get a chance to fully try it as we had to migrate). Rackspace uses a tool called Bit Titan migration tool to migrate email, which we used to migrate my IMAP email to their Exchange account (notice that the new account is in fact Exchange and this may have helped solved the issue).
However, what I was planning on doing, is using their tool (which is in fact created by Bit Titan - https://www.bittitan.com/products/migrationwiz/) to create a secondary IMAP account on my server and move from one account to another. This, because Bit Titan actually detects corrupt emails and doesn't move them so there's a safe chance that those emails which may be causing the issue wouldn't be migrated over. After that's done - and if you have access to the mail server - you can rename the accounts so that all the correct email is actually under the right account. If you don't, I suppose you could migrate it back.
Think of it as using a strainer to leave out all corrupt emails.
I haven't fully tested this solution using the same email server back and forth, but considering all the issues with El Capitan, it may be worth a shot.
Hope it helps!