My friend H. is on assignment in Asia. We iMessage a few times per week.
Last Thursday an iMessage I sent him got rejected:
This only happened when I iMessaged him, and he was still able to iMessage me.
We tried FaceTime and that didn't work either.
He fiddled with his settings and then when I tried to iMessage him I got the iPhone error message: "This person cannot be reached by iMessage at this time"
Best Answer
The reason it was broken: the specific contact had changed his AppleID password and had not updated it on his iPhone.
The solution that worked for us:
He didn't have to reset his network settings, and neither of us powered our iPhones off/on.