Chasing the impossibility?

What should one do when faced with the dilemma of chasing what is in fact impossibility?
Should one continue to fight fight? Or should one just move on and let go?

I think, the degree to which one clings on, really depends on that simple thing called the state of mind. Sometimes, the fight is worth it, no matter how futile you know the result will be and process itself is rewarding enough to remember for a life time. yet sometimes, tis better to let go and just move on.