Hi Kedsgirl,
Graves' disease does run its course and when the immune system heals and stops producing TSH receptor antibodies, the patient achieves remission.
You can achieve remission with meds, herbs, dietary changes, or a combination of things, including acupuncture. You always want to be on the lowest dose of whatever med you're using needed to keep your FT4 level at least at mid-range and preferably closer to the high end of the range. You do this by watching the FT4 and slowly lowering your ATD dose over time. Or your bugleweed dose (Thyrosoothe works well). This prevents the ups and downs you mention.
How long it takes for remission can vary but studies show long-term (average 4 years) of low-dose meds has the highest rate of permanent remission (88%). If you're getting by on a low dose of meds now you may want to experiment with Thyrosoothe.
It's also important to follow a healthy lifestyle. Read some of the posts from JES that are loaded with tips on how she achieved and stays in remission. Best, Elaine