I am having the same problem.
I have a Macbook Pro..brand new. I am using GoDaddy for IMAP services (about 8 accounts).
I have seen that I will go through a bunch of emails in my "inbox" (the consolidated inbox for all my accounts). I will delete a bunch of emails. They disappear and stay gone for a while.
When I explore other mailboxes individually and then go back and click on the "inbox" for all accounts and there they all. All the messages I replied to, moved to other folders, and deleted. It's really bad!
I have rebuilt the overall inbox as well as all the other individual ones.
On a side note, spelling and grammar checking in Safair *****. It never works. Happens in Mac Mail too.
I have been a PC person for decades and am trying to move over to Mac. This stuf makes it very hard to do this. It is continual frustration and I am doing just the easy stuff. Outlook doesnt have any of these problems. Sure, it may run poorly on the Mac, but how much worse can it be from this? Look above, note that the spell check inside of Safari did not catch the spelling errors?
Please help!!!!