I'm worried that if I keep ignoring his sexual demands that he'll get it on with another woman.

Research shows that men are more likely to wander when they don't get their emotional needs met, more than their physical ones. With this in mind, I believe that good open-hearted communication between you and your partner will keep your relationship intimate and satisfying. Tell him how you're feeling and reassure him that you will return his affections, once your libido picks up and be sure to listen to how he feels.