Only you can figure out if this is something you can live with or not.
In any romantic relationship, there is a difference between the things you want and the things you need. Finding out what those things are is more difficult than it sounds. Sure, anyone could sit down and make a list of what would happen in their ideal partnership, but how many of those things on that list are actually deal breakers? As you go along, you might find that one of those traits isn't really all that necessary if everything else is good. Or sometimes you might find you simply must have something you never even considered before. Very few things are non-negotiable - but if you aren't getting what you need, it doesn't matter how many things you are getting that you want.
This is something you are pretty sure isn't going to change, so the only question is: is this a necessity or just a want? If everything in the relationship was absolutely perfect except for this, would you stay? Could you? Would you prefer a relationship that was imperfect but had this element? Sometimes you can't figure out what you can live with until you try. I think, though, that deep down you already have a pretty good idea.
If you decide that it's just a "want" - let it go. mentally categorize it with all the other things that would be nice, but aren't necessary. Like, sure it would be nice if she was a millionaire who bought you a house and paid all your bills, or if she was the most beautiful woman in the universe - but you don't need those things to be happy. OK - those examples are a little extreme, but seriously, I bet if you sat down and wrote out a list of your "perfect" partner/relationship there would be some things on there that you don't have now. Whittle down that list to just the things you need, and throw all the rest away. Appreciate whats really important and let the rest fade away.
Hope that angle helps!