hope sprang eternal

Yes, it is a fixed phrase, because it is a quote from the very famous 18th century English poet, Alexander Pope, from his "Essay on Man":

Hope springs eternal in the human breast:
Man never is, but always To be Blest.
Alexander Pope



Here is some information on Pope:

http://en.wikipedia.org/wiki/Alexander_Pope



Essay on Man:


http://www.theotherpages.org/poems/pope-i.html





The phrase means that the human heart is always filled with hope


(eternal springs are springs which never run dry)

Right to the source! Thanks.

I take issue with this. I believe that the context warrants assuming that Pope used spring simply as a verb meaning to leap, to move upward or forward in a single, quick motion. I don't believe it had any reference to source water.