Again, as similarly answered above, the outcome can be variable, but is often at least two years in cats with no other diseases complicating things, like kidney disease.
Overall, based on the 2006 study referred to above, the best outcome came from cats first regulated with methimazole who were then treated with iodine-131, who on average lived for five years.
Iodine-131 is considered the ultimate treatment of choice for cats with hyperthyroidism since the treatment only targets the overactive thyroid tissue while preserving normal tissue. While surgery can also be effective, the entire gland is removed, and if any stray overactive thyroid tissue is present (which is called ectopic thyroid tissue), continued signs of hyperthyroidism may continue.
While I-131 and surgery are both considered cures for hyperthyroidism and recurrence of the disease is very rare, they are both more expensive options, leaving long-term management of the disease with methimazole the most viable option for many folks.
It is suspected that management of hyperthyroidism with methimazole over the long term still means that the disease progresses, just at a significantly slower rate, likely owing to the difference in outcome using medical management alone versus pursuing a cure with I-131.