Emails being mysteriously deleted

I migrated my company's email from Exchange 2007 on-premises to Office 365 (Exchange 2013 Online) back in April. Ever since then, I've seen at least two cases where emails were mysteriously deleted. Has anyone else seen this before or does anyone have any thoughts?

Both users are using the native iOS Mail app on their phones. In one case the end user read the message on his iPhone on the way to work, and when he got to work the message wasn't in his mailbox. I found it in his recoverable deleted items. Since it was just one item I guessed that maybe he accidentally swiped the message quickly to the left which would delete it. But shouldn't that put it in the trash, not the Exchange Recoverable Items?

In another case, my end user is seeing large chunks of messages (potentially hundreds) being deleted and sent to Exchange Recoverable Items. It sometimes happens during really odd hours like 3:45 AM when he's asleep and his computer is off. If he notices it, he can recover items back to his mailbox using Outlook, but if he doesn't they're automatically purged after 14 days and he'll never get them back again.

This is obviously a major problem, but I'm at a bit of a loss as to what to try. I've asked Microsoft Support, but they basically just want my end users to stop using iOS mail. He's reluctant since he's so dependent on his device.

Thanks for any thoughts you have.