It's hard to imagine a dog at less than 50% of its ideal weight would be running around active for 2 hrs a day.

Regardless... has the Vet run "tick titers" to check for tick borne disease? Did they run a liver profile and check kidney function? Secondary might be to look for digestive enzyme levels, and even run an ultra-sound.

It's encouraging the dog has an appetite, and at that low of weight it should be on free choice. I'd get it off Purina and place it on a high quality dog food perferably the Puppy or Performance formulas which offer high protein and high fat. I use the Propet brand which isn't stocked widely by stores. Some of the higher priced dog foods (you get what you pay for) would also be suitable. If this solves the problem, you can always shift down to a maintenance formula later on. You should be aiming for a 25-30% protein and 10-15% fat dog food for a dog that underweight.

But again before you focus on diet, get the dog tested for tick disease, and liver function at a minimum. Eliminate underlying disease conditions first.