The cut to the chase

How pointless it is to chase after someone determined to get away? Or is it? Or does it depend on what could be accomplished instead of pursuing the chase? Does it depend on who the someone is?

What if it is a something instead of a someone? How about a magical dream that slips out of your mind with the first rays of the sun in your eyes? Is it not worth the chase ? Does the seemingly high probability of failure by itself make the chase futile? How many times does a thirsty nomad have to be tricked by mirages before he should give up on searching for the oasis? Does the constant seeking and losing sight of a goal make the eyes more or less capable of spotting the goal?