Can a relationship work without sex

I am a 33 year old man and I absolutely love having sex. I have been in a relationship with the same woman for several years. Just recently because of medical issues she can not have sex ever again and I find it taking a toll on our relationship. I do not want to cheat on her, but I am feeling the urge to have sex. Masturbation is not an option for me. So, I ask can a relationship without sex work? Or should we call it quits?

No offense, but why is masturbation not an option?

Masturbation does nothing for me

Yes it can work but not for everyone. And I doubt very much if it will work for you. You need to be honest with her and tell her it will not work without sex for you. Maybe she would be open to having and open relationship, maybe even a "don't ask don't tell" type of thing. Since it is not her choice to not have sex with you maybe you could attend some therapy together and find out if there are other things that could keep you two together. But for some people, sex, intimacy, passion are very important and a deal breaker with out it.

If you really love someone, sex shouldn't matter.

33 is too young an age to forsake sex for the rest of your life and since you already feel this way, I doubt if things will work out in the long run for you both. Best to be open with her and decide together. Relationship without sex will work for consenting partners who are a bit more older. Of course lots of adjustment and understanding goes into that too.

There's ways she can participate in sex without intercourse. Is she not willing to explore other options?

A relationship can certainly work without sex. However with your current wants, and if your desires are that strong for it to be a "make it or break it" Deal then I'm afraid it may be. As people have pointed out here, look for alternatives first if you truly want it to work. This desire for sex certainly does make it hard to sustain relationships, since you have to consider that in every relationship, you'll most likely hit a point where sex becomes out of the option. People change in regard to it and when they do it can break your relationship as your expectation has broken. I'm of the opinion true love is personality driven and that her personality should be enough, to others however I understand this is not the case. Sadly. So discuss it with your partner, find some alternatives maybe? Or discuss what you want to do and consider her feelings into it. Negotiate come a neutral agreement and hopefully continue on. If not, and you want to explore more partners that provide sex, then do that. Since you don't wanna linger around hurting yourself cause of it. Good luck with your relationship and have a wonderful day :)