Marriage has its ups and downs. How can it not? It's a life long commitment. If you have been married for longer than a year, lack of sex in a marriage is bound to happen.
Of course when confronted with said situation, our first impulse is to accuse our partner in being derelict in their responsibilities in the bedroom. This approach never really works because it really is a concerted effort to keep the flames a burning. That doesn't mean if you find yourself without "the sex" that it's your fault. It just means that you have to be creative in trying to reach your partner that you said, "I do" to. It's your job and should be your pleasure to remind them to not get too far down the rabbit hole in life. You can do this a number of different ways all of which should stay clear of accusations, character assassinations, if you want to keep your libido demons at bay.
Regardless of your approach, be sure to put all of your cards on the table, without ego. Remember, this is the same person you spent late nights with; the person who had your back, or the person with whom you trust with your life. I know for some this sounds like a bad idea. It makes us feel as though this (first or last) attempt to reach them is in vain. If anything by being open and without ego, you gain a shot of reaching your partner. At the very least for those looking for a way out, you are choreographing an exit strategy. I'm not here to tell you what you want more. That is something best left for you to decide and/or perhaps with the help of our online marriage support group.
So in conclusion, the way to stay faithful in a sexless marriage is simply a choice for the right reasons. Your "right" reasons need to align with how you see yourself in the greatest light. Listen, the choice you make (whether to stay or go) there will be some form of pain involved. You cannot avoid it, therefore the pain you pick should uplift you regardless of how other people view it and thus being without regret. To put it in simplest terms, use the "death bed test". Would you've regretted your hypothetical decision if you asked the question while on your death bed looking backwards at your life?
Good-luck and be well!