@Heartbeat,
I think most people (including most women) would feel the same. For me to be in a romantic relationship without sex would be torture.
I might consider being in such a relationship if I could have sex with other people... but I don't see how that would work. I would be having sex with one partner and not having sex with the other, the non-sexual partner would feel like nothing but a close friend.
If you are asking for an exclusive relationship with no sex... you are telling your partner that he needs to be abstinent. For most humans, this is not a reasonable request.