That's not rendering the marriage due, JW mates don't have to put up with that crap. They can get the elders involved (yes, I know this is terribly intrusive, but if you are going to be trapped in a crazy fundamentalist religion that dictates all your life choices, you might as well take advantage of it when it can work in your favor). If the mate doesn't accept the counsel, the mate who's being deprived should be able to get a separation.
At that point you're supposed to wait for the other mate to be seen with someone else, but unfortunately if you're dealing with a true asexual nun, then she may just keep to herself as a woe-is-me-I-guess-I'll-just-spend-all-my-time-in-service spinster, and you're stuck in the marriage without getting proof of infidelity. At that point I guess the only option is getting divorced anyway, getting DFed, and working to be reinstated.
Personally I don't have much interest in sex, but hell if I would put up with that from a marriage mate. A close relationship needs sex as a bonding tool. Unfortunately this somewhat exploitative use of the JW system that I described above is not something that comes naturally to sincere JWs, even if the lack of sex is hurting them emotionally and causing stress from a pent-up libido. All of us born-ins in particular were conditioned from childhood to just soak up capricious punishment and emotional abuse.