For quite some time, I’ve noticed that iMessages and phone call notices get lost, if they come in while my iPhone is turned off. I turn my phone off overnight.
Today, when I powered the phone on, I saw imsg and phone call notifications, briefly, just after I entered my passcode.
When I looked in iMessage for recent messages, there wasn’t anything new. The same goes for recent missed phone calls.
A few hours later, I started using my iPad and noticed an imsg came in.
This was in response to a “Happy Birthday “ message I sent the night before (to a friend who doesn’t have an iPhone).
I then checked my iPhone again, sit still had not shown up.
This continues to happen from time to time, when I power on my iPhone.