I was looking a list of challenge rewards (I wasn't aware there were any), and saw that you could undertake certain challenges once you reach a certain rank on your Chocobo.
Got it.

The question - do you have to do the challenges each time you breed out and get a new choco, or is it something you need to do just once and you'll have that reward unlocked forever on any bird you take?

I'm looking at YOU, Super Sprint!