I would divorce my wife, the mother of my children, the woman who I have been with for over 12 years, the love of my life, IF she were suddenly unable to have sex with me.
Depending on the circumstances, I may not divorce her right away. If she was hurt, I would provide her with support, but at some point, our relationship would be over.
If this girl really does want sex, and you are unable to give it to her, your relationship is doomed.
If you have no sex drive, I highly recommend that you see your doctor, the problem may be purely physical, and he might be able to help.
Being a guy past puberty, and not having a sex drive means there is absolutely something wrong about you. Well maybe "wrong" is not the right word, if this is at your core, then I would say it is how you are naturally, but it is definitely not normal.
As a guy with a normal sex drive, I honestly can not see why you would even want to be in that kind of relationship. I can understand the desire for relationships, but for me if there is no intimacy, then I would just consider it a friendship, and there is nothing wrong with just being friends. That is just me though, I have never NOT had a sex drive, so I don't even know what that would be like.