He may have a food allergy. We've only just discovered that Hot Rod is allergic to chicken. Most puppy food is chicken and then each time a dog has an upset tummy, chicken and rice is advised. Plus he just plain loves chicken!
We didn't give him any for a while and then we noticed that the couple of times we did, he would start licking and kinda nibbling at his paws. We stopped chicken, he was fine, gave it and he started again.
Is it possible for you to try and weed out different ingredients? So many dog foods have chicken/turkey/duck in it.