An adjective to describe a person who has come back from failure

Solution 1:

"Resilient" seems to be a perfect fit.

  • able to become strong, healthy, or successful again after something bad happens
  • able to return to an original shape after being pulled, stretched, pressed, bent, etc.

merriam-webster.com: resilient

Solution 2:

Perhaps resurgent

rising again, as to new life, vigour, etc.

Collins

The term is especially apt where there was a lull or quieting of activity before the renewed effort.