Mine-kun is Asexual

Mine-kun is Asexual. He doesn't like sexual intimacy in a relationship. He can kiss a girl, but it's not something he wants to do if he can help it. But Murai loves him so much that she's willing to overlook the fact that she can't hold his hand; that she can't cuddle up next to him when they watch movies together; that she can't fall in love with him the way that she hopes to be loved in return. In the eyes of those around them, is this even a relationship that's meant to last, or is it a train wreck just waiting to happen?