Several times now I've opened up Apple Mail and been dismayed to see Mail removing the emails in the Inbox without my doing anything. The emails aren't deleted, they don't go to Trash, they just vanish and disappear for good. It's enough to make me consider switching to Outlook.
I think the problem is to do with the clever synching across devices, but it may not be an Apple problem at all. The emails may still be visible on another device if one disconnects it from the Internet first.
It's not a perfect solution but keeping the Inbox empty is a good approach. Deal with emails as they arrive, set reminders to deal with things later if needed, file the emails locally out of harm's way.