FWIW I have been in three LTR's, (marriages), lasting over ten years, all with straight men.  My current LTR is going on 15 years of which we have been married since '07.

So yes, provided you meet the needs of your partner and he, (she?) meets yours, then your chances for a meaningful LTR should be the same as anyone else's, all things being equal which they are not.  Appearance, demeanor and personality will all enter into the equation.