Hello, my name is***** and I have over 20 years of experience as a veterinarian. I'm sorry to hear that your little one has luxating patellas.
Unfortunately there isn't an external wrap that will work to hold his kneecaps in place or help with the pain.
With this disease process the groove that the knee cap sits in is so shallow that the kneecap simply sides out of alignment. No amount of external force can keep it in place if the "place" is no longer anatomically there. His "hop" is likely an attempt to put his knee cap back where it should be. That often works in the early stages, but over time as more arthritis occurs and the groove where the knee cap should sit becomes more shallow it no longer works well.
This condition is usually congenital, meaning the puppy is born with the genetics to develop the condition as they grow. It doesn't mean that the pup is affected as soon as they are born however, and in most cases it is a condition that we see develop as the bones, ligaments and tendons that form the knee joint grow and develop or in an older pup that gets arthritic. Not all pups in a litter are necessarily affected.
If your fellow has this he could benefit from joint supplements such as glucosamine/chondroitins and omega 3 fatty acids or a supplement called Duralactin as well as pain medication. I do think that he has a fair amount of pain because he is carrying his leg and no longer jumping.
I understand that he is on a joint supplement (Advanced joint), which likely has a glucosamine/chondroitin component in it but does that have omega 3 fatty acids too?
Rimadyl (carprofen) is a nonsteroidal anti-inflammatory that works well for some dogs, but others do better on Meloxicam (Metacam), so it may be worth trying that.
We can also add Tramadol for pain, which complements a nonsteroidal in controlling pain.
My usual protocol for dogs with conditions that cause chronic joint pain and arthritis is as follows:
Long term for any joint pain I recommend using a combination of a glucosamine/chondroitin product (examples are Dasuquin or Cosequin) and an omega 3 fatty acid (like 3V Caps or Derm Caps). I recommend an omega 3 fatty acid dose based upon the EPA portion (eicosapentanoic acid) of the supplement as if we do that the rest of the supplement will be properly balanced. Give him 20mg of EPA per pound of body weight per day. For example a 15 pound dog could take 300mg of EPA per day.
Omega 3's and glucosamine/chondroitins work synergistically and improve cartilage health and joint fluid quality and quantity as well as reducing inflammation. They can take several weeks to see full improvement but some dogs do very well with them alone. They are available over the counter.
Another option is a product called Duralactin. This is an anti-inflammatory product derived from milk proteins and it also has omega 3 fatty acids incorporated into it which can be very helpful. See this link for further information: http://www.duralactin.com/products_canine.htm
If those medications are not enough veterinary prescription drugs that are more potent include a nonsteroidal like Metacam, Deramaxx, Previcox or Rimadyl. If those aren't enough we can add another drug in the opiod family called Tramadol and/or another drug called Gabapentin.
If you'd like to read more about pateller luxations here is a link to an excellent article written by the American College of Veterinary Surgeons: http://www.acvs.org/AnimalOwners/HealthConditions/SmallAnimalTopics/MedialPatellarLuxations/
In mild cases some dogs learn to kick their rear leg and pop the knee cap back into place. Over time however because of the constant wear and rubbing of the knee cap moving in and out of place we see secondary arthritis forming. Whether he needs surgery or not now will depend upon how severely he is affected. In most cases the dog does need surgery at some point. Given that he doesn't want to jump anymore and is carrying his leg surgery may be the best option for him now if supplements and medications are not enough to control pain.
Best of luck with your pup, please let me know if you have any further questions.