Most of the time, if the panting is caused by physical exercise or stress, the panting should stop any time up to about 15 minutes. If a cat is panting for more than 15 minutes or so, and if the cat is showing other symptoms of ill-health, then that’s a sign something else is causing the cat’s symptoms. I would advise you to go to the vet if your cat does not stabilize its breathing 5-15 minutes after stopping physical exercise.