Why should a person stay in a sexless dating  relationship?

Logically, there is no reason to be in a relationship if you are not having sex.

Masters & Johnson and the Kinsey Institute have reams of research (all of it recent) saying that men and women are equally interested in sex.  

53. "Shame on the fools infatuated with love for women. Women are like nothing but birds flitting above the tree tops.
36-38. "In secret that woman introduced her son to my friend. That son was an ignorant fool with eyes blood-shot with drink. And my friend went on enjoying him in my very presence. But she, though completely overpowered by him and being enjoyed by him day after day, never left me, and I, too, did not abandon her. And out of that union was born a fool of the same type as his father.
50. "Similar is the fate of the people who, deluded with the quest of happiness, have fallen into the snares of the task-master of action. They are bewildered in their frenzy and destruction awaits them .
Tripura Rahasya 

Love and respect is what keeps them together