I think its possible for you to have a close relationship and NOT fall in love. And its also tragic when that happens and you want something more out of it. I learned the hard way that just because a guy and a girl are close doesn't mean they will fall in love. Or one might and the other one won't...Kinda frustrating.
I however don't agree a relationship can remain static. Even if the two people never fall in love, their relationship will surely change. It will get better or worse. They might grow closer or just fall apart completely. No human relationship, whether it be friendship, family, love, or even enemies; stays the same forever. I wouldn't say it HAS to change...but I would say change is eventually inevitable and the longer you try to keep things the same the worse it will be in the end when they do.