Mail Disappears off iPad after I access my mail on Mac

Question

I have a MacPro desktop, iPad, and iPhone, all tied together, all running the most recent updates.  Recently, my iPad was acting up and not retrieving my mail on my main account.  The other devices were (and continue to be) just fine.  I deleted that mail account off my iPad, then added it back in.  Email began behaving and getting delivered just like always EXCEPT if I then check email on my MacPro.  Once I do that, all inbox email associated with my main account, both read and unread COMPLETELY disappears off my iPad.  Even if the message is flagged, it is gone.  Everything stays put on the Mac and the iPhone until I delete it or otherwise.
I searched these communities and thus far have tried shutting down all background apps, restarting (multiple times) and changed the delete messages setting to "never", which really should only matter to trashed messages, not those sitting in my inbox.
I checked the "server port" on my phone and compared it to the one on my iPad.  They were different, so I put them both on the same one as the iPhone.  The message showed up on the Mac and on the iPad, but as soon as I refreshed the mail (such as to update), **POOF** the message in my inbox was gone on the iPad.
I would be most appreciative if someone could offer me insight as to why this occurs and how I can fix it.  Likely it is some squirrelly setting I haven't discovered yet, but I am hoping one of you geniuses out there can set me straight!
Thank you in advance~

Answer 1

Well, cripes.  My husband just saved the day for me.  We had to force the iPad to take a POP account.  Here's how we did that:
Create a new mail account on the iPad with a bogus email address and a different name from your problematic IMAP account.  In my case, I doubled up on a number that is part of my email address.  Thankfully, nobody else had that email address
When the iPad refused to add the account because it was a bogus email address and came up with the error message, THEN it let me choose the ability to add a POP account. 
I was able to edit out the extra number from the bogus email address to my true email address.  I had to do this in three places: the main account name, the inbox info and the outbox info, and take out the "IMAP.xxxxx " part and replace it with the "mail.xxxxxx" entry that goes with my POP account (that was listed in the settings on both of my other devices that were behaving: the iPhone and the MacPro).
Now you should have two accounts for the same email address (with two different names) showing on the iPad.  Go back through mail settings and "DELETE ACCOUNT" for the IMAP version that was screwing everything up.
Inbox messages should now stay on your iPad because it is using the same type of account the other devices are.
Apple, why in the name of all things good and electronic would you make it a default to IMAP without an obvious way to choose to do a POP?   Good grief I had a week of stress over this whole thing and nobody else seemed able to figure it out either.