In my opinion it has to due with the life he lives. Being a rock star and travelling all the time makes it hard to have a girl friend. I believe Matt is saying that he doesn't mind being on the road and still having a girl... but his girl can't take having him gone so much. When he says "I don't mind, but I'm not surprised to find that you do", he's saying that he knew that they may run into this problem of him being on the road his whole life. And when he says "So I guess that I'll curl up and die too", he's expressing that he loves her and wants to make her happy.. even if it means dying.
In my opinion it has to due with the life he lives. Being a rock star and travelling all the time makes it hard to have a girl friend. I believe Matt is saying that he doesn't mind being on the road and still having a girl... but his girl can't take having him gone so much. When he says "I don't mind, but I'm not surprised to find that you do", he's saying that he knew that they may run into this problem of him being on the road his whole life. And when he says "So I guess that I'll curl up and die too", he's expressing that he loves her and wants to make her happy.. even if it means dying.