Have you checked his toenails? Might have a thorn in his paw.....
I noticed this same thing with Ellie, and I was about to make a post about it. Just today she started limping really,really badly to the point where she can't put her leg down sometimes, and if she does, it won't always hold her weight (a very healthy weight for a puppy). It's her front leg. The limp goes away with exercise.
Phoebe has the same limping going on and usually it is better with exercise. A couple of days ago she was playing hard with her corgi friend and afterwards was limping. Yesterday she stayed quiet all day but today has been running, although unevenly with the limp. I wonder if it is common with growing puppies in growth spurts as this has gone on pretty much on and off since we got her. She's close to 6 months old now.
I wondered that too, Sarah. Particularly because of exercise making it better. That's not how injuries usually work. Ellie was perfectly fine on Sunday and has been since then.
Just went through this with my 1 year old Linus. He would limp only when he woke up, or after laying down for a long time and then once he was up it was like nothing happened. We tried just leash walking and making him rest for a week and it got much better but then we played with him and it was back with a vengeance. We ended up taking him to the vet who said it was probably a muscle pull. He gave him anti-inflammatories which really helped along with the leash walking and rest and carrying him up and down stairs. He was fine after a week this time.