Or maybe they have, and just aren't sexually attracted full stop.....Some people who feel “asexual” might just not be exploring aspects of what excites them.
Asexual does not mean frigid. I describe it as a state where sex is not at all important, but can happen spontaneously as part of a relationship where the partner requires it. Another expression of love, maybe?
Should the Asexual split with their final partner, that function is then superfluous. An Asexual life may be the winding down of what was once a requirement to live in a needed way. To do what was required. The energy can be used elsewhere, so why not?
http://www.calmdownmind.com/understanding-your-sexual-energy-and-sexuality/