Usually a low dose of l-thyroxine is used on a daily basis in these cases. You might want to check out the Pet Care Forum's Veterinary Hospital area. You might find information there on this problem, as well. I am not sure why this recommendation was made. It is possible your first vet knows something I don't.
Hypothyroidism is unusual following radioactive iodine therapy.
Once in a while it takes two doses of radioactive iodine to work but that is an infrequent occurrence as well. Dear Doctor - thank you for being online. We have a 15 year old male cat who lives indoors, travels with us, and, in short is our daughter's little brother. Last October, as we were preparing to move from Portland, OR to Washington, DC, we took the cat to have his shots updated. However, he had been sick once before in Oregon, and blood work had been done.