Not to revive a somewhat dead thread, but I recently bought a brand new MBP Retina 13", and I was experiencing this same issue. I have an iCloud account, two Gmail accounts, and a university IMAP account set up in Mail, and all accounts would frequently lose connection throughout the day. Connection Doctor didn't provide any useful information, and I tried many of the suggestions found in this thread and others with no success. I was also getting random "timeout" messages from iTunes throughout the day (an issue I've seen others complain about in other help threads) when I wasn't actually doing anything in the app (it's just open in the background). Because of this, I figured that maybe it had something to do with the wireless adapter, and since the laptop is brand new, the most obvious explanation seemed to be a manufacturer defect. (As a side note, the mid-2011 MBP 13" that I upgraded from NEVER had this issue and was running the same version of OS X El Capitan, which made it seem more likely that it was a hardware issue).
Really not wanting to have to go into the Apple Store and hope that my computer would reproduce the error to allow the technicians to troubleshoot it (it happens so erratically that I figured with my luck Mail would work perfectly at the Genius Bar...), I decided to try one last thing that everyone talks about when hardware seems to be acting up: resetting the PRAM/NVRAM. I'm pretty sure other threads about Mail issues have mentioned trying this and not seeing any results, which is why I put it off for so long. Well, I think it might have worked. I'm now a full 24 hours with no Mail disconnects or iTunes "timeout" messages. I know that this was a lot of info to get to the solution, but I thought it might help some people in the future who are searching Google for solutions to this very specific, very odd error.
TL;DR It might not work for everyone, but try resetting the PRAM/NVRAM. So far (24-hours in) it's working for me.