Hi Myra,
The thyroid doesn't burn out in Graves disease although after many years without treatment, if Graves' disease remained active, which is rare, the gland could atrophy. The normal course of Graves' disease is a move into remission with normal thyroid function remaining.
About 20% of patients can move from hyperthyroidism into mild hypothyroidism, but this type of hypothyroidism is very mild compared to hypothyroidism caused by RAI. And this type of hypothyoridism can resolve on its own similar to the way hyperthyroidism does. Hypothyroidism following Graves' disease isn't caused by glandular failure. Rather it's caused when people start making blocking rather than stimulating TSH receptor antibodies. Best, Elaine