Hyperthyroidism is a very common disease of older cats. It may cause weight loss, vomiting, a rough coat, heart troubles, and a number of other problems. There are three ways to treat the disease: medication (known as Tapazole), surgery, or radioiodine therapy.
Most people start by treating their hyperthyroid cat with medication. And, for many cats, this treatment works out well. In other cases, complications arise. Some cats experience side effects from the medicine. Others, such as Jasper, have a low tolerance for late doses. The vomiting cycles that you describe are unpleasant for him. They are also bad for his health.
When Tapazole treatment does not work perfectly, it is not unreasonable to consider the other two options. Surgical removal of the thyroid gland usually cures hyperthyroidism permanently. However, it is not without risks. Cats must be anesthetized for the procedure. Postoperative pain is common. And, in rare cases small glands located near the thyroid gland (the parathyroid glands) are damaged or accidentally removed along with the thyroid gland, leading to fatal blood chemistry imbalances.
Radioiodine therapy is a newer form of treatment. Cats receiving this treatment are injected with a small amount of mildly radioactive iodine. The iodine eliminates excess thyroid gland activity.
Most veterinarians (including me) believe that, in most cases, radioiodine therapy is a better choice than surgery. Usually, radioiodine therapy cures hyperthyroidism permanently. No anesthesia is required, and the procedure is not painful. The biggest downside to the procedure is that cats must be hospitalized at a special facility for a few days while they eliminate the radioactive iodine. However, that downside is not unique to radioiodine therapy–many vets also recommend several days of hospitalization following thyroid surgery.
Jasper may be a good candidate for radioiodine therapy. I recommend that you talk about the pros and cons of the procedure with your vet.