really need advice - do we split or stay together?

This is my first post here, I could really do with some help and advice. I'm 37, I've been with my girlfriend for over 4 years, we live together and have a really nice life generally - except for one thing.

We were friends before we got together, and partly because of this, our relationship has never been particularly passionate or sexually driven. We rarely have sex at all, and when we do, it's not great. It's like we are compatible in every possible other way, but sexually it's just never been quite right. I'm pretty sure we are both aware of this, but the rest of our relationship is so good, that it's almost impossible to think about breaking up with each other. I love her and she loves me, we are pretty much inseparable, but this sex thing is not getting any better. I find myself thinking about other girls, and I'm sure she has similar thoughts too. We have both been in more passionate relationships in the past with people who we were compatible with sexually, and not in other ways. This relationship is the opposite of that - we are practically perfect for each other - except for the sex.

I really don't know what to do. She is rejecting me sexually, and I'm not sure if I even mind that much any more. I miss passion and romance desperately and I am worried that if we carry on like this, I'm going to end up cheating on her, or vice versa. Is a sexless relationship based on friendship worth salvaging? Can sexuality ever be restored? I suspect the answer might be 'no', but if the answer is yes, how? I'm 37 and don't really feel like chasing girls around any more, but I also don't want to get stuck in a sexless relationship for the rest of my life.

I'd really appreciate any help / advice you may have.