
With the correct antibiotics, steroids, proper care of any open sores and loads of TLC there is no reason your pup shouldn't go on to have a full and happy life.
Having had a Papillon pup at 12 weeks with Pyoderma (developed 1 week after her first vaccination) I wouldn't have any hesitiation in caring for a pup who had it again. It is easier said once you have experienced something though.
Edited to add:- Ellie died at 14 months old due to an accident, but I have now doubt that as our vet said she could have easily lived her normal life span without any ongoing problems due to her having had pyoderma.