I checked some things out last night after re-reading these posts. Here's what I know in regards to godaddy imap issues on Yosemite and my situation:
-My iPhone gets the mail perfectly except godaddy doesn't push anymore, I have to manually check mail on my iPhone but it is always up to date and synced with what has been read on my other 2 computers and new mail messages (WITHOUT RESTARTING THE APP)
-My 2009 MP and 2013 rMBP both up to date on Yosemite have the same issue, if I check mail anywhere else it doesn't sync the new, read or flagged messages until I restart the mail apps where I'm looking.
-It's only an issue when I check mail somewhere else while leaving my mail apps open on the laptop and desktop (obviously if they were closed, they work properly when I open them)
-All of my mail/port info is the same on all 3 (it wasn't yesterday but I fixed it and all are on 993 but still have the issue)
-I turned of iCloud mail syncing to see if it was the issue and I still have the problem relying on just imap and godaddy
-Starting with Mav I've removed the accounts and started over several times and nothing changes
-I have 3 gmail, 2 exchange accounts, @me.com and none have a single issue after the latest Yosemite update (Exchange was wonky at first with Yosemite)
-When I was working on a fix in Mavericks I read some interesting info that helped my case immensely then but didn't totally fix it. I read that too many inquiries from the same IP to godaddy's server might be the problem. As in 4 iPhones, 2 iPads, 2MP's, 2 rMBP's all getting mail every minute with the same IP can be an issue with godaddy. Not sure if it has anything to do with this but in Mav I put everything I could (non essentials) on Verizon LTE and the missed mail issue rarely happened.
-At least with Yosemite I feel like I have a process so I don't miss any new email but this is unacceptable. I've been trouble shooting syncing with Apple since .mac and this is by far the worst it's ever been, and progressively worse since Mavericks - and MAIL of all things is the issue now. Ten years ago the only syncing problem was the colors on my iCal. I buy apple products for my business because they play nice together and this continues as an unresolved issue of maybe the most essential function of the devices involved. I don't care who's fault it is godaddy or mac, it just needs fixed by professionals. Why even test the OS? Just put it out there and let us troubleshoot it... I'm sure apple has the resources to get mail to work properly on their OS and iOS and I'll be holding on to my budget for nMP's until I see a change.