Has your friend checked with some other people to see if this problem is on your end...or his?
I don't think he's checked with anyone else. Unfortunately, he's so technically incompetent that it's impossible to discuss these things with him. So, I'm trying to get some ideas before I discuss it with him. If I don't have a quick and easy solution for him, he won't be interested in fixing the problem.
I'm assuming (maybe incorrectly) that since I haven't had any problems texting anyone else, I don't think the problem is on my end.
It almost seems as if he powers his phone off whenever he's not using it. But even so, when he powers it on again, any pending unreceived message should then come in to his phone shouldn't they?
I was wondering if iOS has some kind of "ignore" option to block messages and calls from particular people, that he may have inadvertently activated. I've never seen anything like that, but then I'm not an iOS power user by any means.