The issue: we have a client who was migrated from our on-prem Exchange servers into Office 365 and Outlook in the cloud. The client is an iPhone and iPad user, with his mailbox setup on both in the Mail app; all was well until this last weekend.
At that time, he noticed that if the mail app was closed, or was not the foreground app on his iOS devices, mail wasn't being delivered to the device - when new messages arrived, the unread message indicator in the app badge was not incrementing and when he opened the Mail app, a number of messages would be delivered.
So in effect, if he doesn't keep the mail app in the foreground, and check it manually, new messages aren't being delivered and he's not keeping up.
We confirmed mail settings for his Exchange account were still set to Push; we added his Exchange account to another iPad and another iPhone, and the same symptoms were exhibited there. We put another Office 365 account on that same iPad and the issue did not affect that user.
Open to your ideas and thoughts - anyone seen this, before?