I'm still hoping someone that has experience with this will reply but until then, I found this information from Dr. Karen Tobias (a reknowned Vet in this field):
Usually after 1 surgery (where the shunt is not completely closed), the pup is better within 6 months of being on a special diet. In some cases, a 2nd surgery is needed to completely close the shunt and a few more months is needed for recovery and to be weaned off the special diet.
You can read her info and some research here:
Liver Shunt Research