Life is a personal journey.
No one can keep someone from having sex with others. They can only stop you from having sex with (them). Staying in a sexless relationship/marriage is a choice an individual makes.
Not long ago I asked "Is sexual incompatibility enough of a reason to end a marriage/relationship?" Over 90% answered saying "No".
However I suspect if I had asked; "Would you rather your mate leave you or cheat on you?" My guess is they would have chosen to have their mate leave!
Essentially it's the same question depending on who is frustrated.
In my opinion it's unrealistic to STOP doing something and expect things to remain the same.
If one stops going to work they'll lose their job, stop paying the rent/mortgage they'll lose their home, or if they stop eating they'll die. If someone decides to stop having sex with their mate odds are he/she will either leave them or cheat on them at some point.
“While we are free to choose our actions, we are not free to choose the consequences of our actions” – Stephen R. Covey