I sympathize with this man's feelings as my husband and I have experienced the same feelings of frustration during my fertile times. Though we know in our hearts the ultimate good of NFP, the day-to-day practice is often something we inwardly curse as we try to avoid each other so neither of us must be the one to say "No." We have never until recently had serious reason not to have another child and so have not had to practice abstinence for long periods of time.
I don't know what this man's situation is or how many children they have, but it seems there are other issues here within the marriage as well. My husband never has to "ask" for sex. We try to remain thoughtful and charitable even when we can't be together, even when we are truly desiring a physical relationship. It doesn't sound as though this man's wife has made a full commitment to NFP or the marital relationship since the beginning of their marriage. It is unfortunate that all the negative aspects of their marriage are being blamed on NFP and lack of sexual relations. There is so much more to a marriage than that!
In closing, I guess I will say that I hope this couple seeks help and finds the beauty in NFP and their marriage. My husband and I will soon be practicing what we preach as after baby #9 comes along in August I feel strongly compelled to use NFP to avoid pregnancy indefinately. It will be a challenge for us and I hope other couples will pray for us as we take on this responsibility.