I think if I was being ignored by my partner I would want to know what is going on.
Replying by threatening to leave during exam time is just laughable.
But of course there is more to it than OP has said.
Yeah but the constant texts/messages. Go back to when you had exams and imagine the constant bombardment of texts when your trying to revise. It would **** me off and I would feel smothered.
And the fact that she doesnt reply so he sends another saying I love you. Now yes I think it is nice that he does and tells her that but not in this situation. She doesnt seem interested at the moment, like I said it could just be the pressure of the exams, I mean heck we've all been there, so its just going to make him feel worse IF she does decide to break up