Does anyone out there ACTUALLY believe that a long distance relationship can work?

The only replies I've so far gotten in regards to my long distance relationship can be summed up in three words: "it won't work".

Is there anyone out there that actually believes that love can conquer all, no matter how far apart you are? I don't think of myself as some naive idiot who thinks that love is all about roses and rainbows and butterflies and other BS like that.. relationships in general take a lot of work, but I'm genuinely disgusted by the amount of answers I've received telling me that my boyfriend is probably out cheating on me right now (despite us already having lived apart for three years).

Are you all just cynics? Or is it just a matter of laziness - that you don't want to put in the effort to make a relationship work if you're a province (or state) apart?

I believe in love, and I believe that if both parties are willing (as is the case in my own relationship) a long-distance relationship can work, despite the obstacles.

Is anyone with me? Or am I the only optimist left?