I am going to go right to the heart of the manner by offering some thoughts about this situation, but want to suggest that your boyfriend see a cognitive behavioral therapist to take care of the mechanics behind unraveling this. That being said, let me offer you my thoughts and experience.
In treating panic attacks like this I find it extremely helpful to first identify what the panic attack is for the person. It has always been a fear of loss, separation or death that has been promoting it. It is the fear of losing something that generates the panic and in more cases than not the fear is a type of separation anxiety. My best guess is that the fact that they are getting worse as you come closer is very telling. It isn’t about the anxiety of becoming more intimate. It is likely to be about the anxiety of losing the intimacy. The closer you get to what you want — the more you fear losing it.
That having been said, the mechanics of how to slow down the reaction and keep it at bay are best carried out with a qualified cognitive-behaviorial therapist. The research on its effectiveness in treating panic attacks is good. The Find Help tab at the top of the page can help you find a therapist with that specialty in your area.