Outlook.com/Hotmail randomly disappear minutes after arriving or being read the first time

This is so frustrating to try and solve, because random emails will be available for sometimes minutes, sometimes hours and then simply disappear.  Let me give you some background (hopefully this can help)

- Have a hotmail.com account (paid version)

- Have and iPad with the hotmail account associated with it (as well as a corporate exchange account

- Have an iPhone with the hotmail account associated with it (as well as a corporate exchange account

- Have Outlook 2010 with the hotmail account associated with it (Using MAPI) as well as a corporate exchange account

Scenario 1:  On the iphone/ipad/outlook, an email will arrive, you can see the email, read it, and litterally it will just disappear, it didn't get moved to a different folder, not in deleted items, etc.  Completely gone.  Even a search of the entire box shoes it missing.

Scenario 2:  On the iphone/ipad/outlook email comes will arrive, and w/out opening it you simply see the header and the 5 lines it displays (subject and some of the body) and again, the email just disappears.  Didn't even get a chance to open it.

Scenerio 3:  Same as Scenerio 1, except its there for a short, random time (about 3-4 hours), no problem, you reply to it, etc.  Later you go back and its missing, completely gone.  Again, not in deleted items or other folders, you can check on both the ipad, iphone, Outlook, etc. and its totally gone like it never ever came in.

The challenge is that its random emails from senders that have been sending for years, and other messages they've sent before and since are there and stay there.  It happened this morning 3 times, and last week twice, but there is no rhyme or reason to it.  

I've wondered if it was something with iCloud, but why would it delete some and not others (and iCloud email account isn't even being used).  The iPhones are the iPhone 5 and are up to date.

Any help would be great!!

Thanks!