I fear (and apparently, quite justifiably, according to what I have been told) that creativity is finite.

Now, everything is finite in it's own way, I understand that... If you don't believe me, think of something so practical as an example such as, sunrises... how many times will the sun rise?  Not just in out lifetime, I mean ever.  It is a finite amount.  The sun is going to explode one day.

But I fear my creativity is finite in that I will only be creative x amount of times before I suddenly am unable to be, and I will become old and boring and uncreative.  Is this ridiculous or justifiable?

It doesn't matter... it's just one of my top fears.  Being uncreative.