I would stay and have sex with other people. With his blessing, of course.
I’d stay with no sex only as long as there was an agreement that I was free to get sex somewhere else. Given that I am not and never have been much of a ladies man, this probably means ‘no sex’, but hope is a wonderful thing. 
I think I’d have to be faced with it before I could answer. I’d like to think that I would stay, no matter what. I just don’t know.
ETA: female.
At 73, married for 46 years, I will stay no matter what.
I’d stay if it were for physical reasons. If I loved him, then I’d find a way to deal with it (not involving cheating). Sex is important to me, but so are other things.
If it were for emotional reasons, I’d stay if he were willing to work on it. If he wasn’t willing to work on it for my sake (and sex is important to me), then I’d have a hard time staying.
What if he didn’t give you his blessing?
Dammit, Dio! Beat me to it.
Well, he would, there is no question about that, but if for some reason he wouldn’t, then… I’d stay. I guess I’d just masturbate an awful lot. It wouldn’t be the same, and while I do love sex, I love him more, and can’t imagine not having him to share my life with.
If it were the relationship I have now, and it was due to something physical, then yes, I’d stay. I love the sex we have but it’s only one part of our relationship. I can’t imagine him denying me sex just because he doesn’t feel like it. If that were the case there would be something seriously wrong with us.
The OP says a hypothetical “average” long term relationship, though (I rate my current relationship as well above average). I don’t think I’d stay if that were the case, unless there were children involved. Then I might consider it.
I have lots of wonderful relationships without sex, they are called friendships.
My partner and I have discussed this, and we immediately agreed that we would never separate, but would instead invite a third person to join the relationship . . . someone we both loved and trusted, who would be comfortable with both of us in general, and with either of us still having sex in particular.
And we’re pretty much in agreement as to who this person should be. 
Female, if it were a physical condition and depending upon the situation, I would probably stay if we were in love and loved each other. If it was due to the other person losing interest or for some other reason, nope, I’d leave. (51 year old woman here).
Arrendaja and I haven’t touched each other for almost a year. I’m committed to staying long enough to raise Arrendajito - we’re almost there. Then we’ll see. I have a large loving circle of friends to keep me sane, and while it’s infrequent, I don’t go without sex entirely. Arrendaja is an easy person to live with, and there are good reasons for staying married even without sex. We give each other plenty of room. I’m not miserable.
My dad is in that situation now with my mom. If he left her, I would think he was the shittiest person on earth. If he cheated, I’d think the same.
The fact that this option seems to be extremely rare proves to me that the Dope and Morality don’t mix.
You guys keep saying that sex isn’t that important, but apparently it’s so important you couldn’t live without it. You’d rather cheat. That is selfishness, pure and simple. I’d actually argue you don’t love the person you’re cheating on.
NETA: That’s reserved for those who would cheat or leave. Love is about putting the person you love in front of your own desires.
I don’t think it’s that simple. For me, sex is only one part of my love for my partner, but it is an important part. I wouldn’t leave him just because that one part wasn’t working out, but the sexual aspect of a relationship rarely exists in a vacuum. I can’t imagine a relationship where EVERYTHING else is working just fine except for the sex.
A month or so ago I was listening to Dan Savage’s podcast and there was a recording of a girl who was talking about her mom, who had to take care of her invalid dad for years and years. Her dad was dying of some terminal disease and it not only affected his body but also his personality. He became a mean and selfish person over the course of his illness, but his wife saw him through to the end. But his wife also started seeing someone else during his illness because she was starved for affection - something she could no longer get from her husband.
Was it selfish of her? Maybe to some extent. But would you argue it would have been less selfish of her to have been honest about it and simply leave her husband in the middle of his illness? Or should we expect her to be an angel about the whole thing and completely sacrifice her happiness and sanity for the sake of her husband, who arguably was not the same person she married once the illness started affecting his character? What about the possibility that her husband doesn’t love her anymore because of how the illness has affected him?
I don’t know what I would do personally in such a situation, but I can’t say I can find it in my heart to condemn the woman who took care of her husband until his death yet couldn’t help but seek some affection elsewhere at the same time. I don’t think love should mean sacrificing your own happiness and sanity for the sake of the other person.
I’m not sure what “average in all regards” means. Is the “average” relationship pretty good or pretty crappy? Don’t a significant number of relationships end in divorce/breaking up (which doesn’t really match with the “no matter what” options)?
Dude you’re twenty… and I’m seriously not being condescending towards you… but you’d be amazed how many adult couples are living like this sans the physical ailment…
You know I think it was Oliver Wendell Holmes that said bright line law makes bad law. There’s absolutely no way IMO that you can qualify everyone under your ultimatum. Relationships are complicated and messy. Like the aforementioned story about the Savage podcast. That woman saw through what she believed to be her commitment… but according to you edict… she’s somehow unworthy? Even removing the illness… debilatating circumstances… a human being has a desire to affection… you’re simply expecting people not to breathe…
No I wouldn’t. I’m perfectly aware that there are a bunch of couples out there not having sex or swinging. He said he’d have to get sex elsewhere and I was curious if he would allow the same for his wife. My age is irrelevant.