Investigation dropped or not, if you buy a stolen dirt bike they take it from you and return it, you can claim stupid and not be charged. The same should work for in the case of the dog. If there were no leads, and after six months it's understandable there wouldn't be, the case of the original theft and re-sale would be dropped, but ultimately it's my dirt bike, you don't get to keep it just because you didn't steal it, and the case was dropped.
I would be returning the stolen dog as well, or at least replacing it with a new puppy, in this case, since I had the dog longer then they did.