What are your actual thyroid hormone levels, at present? You should be getting tested regularly for Free T3, Free T4 and TSH. If you have current labs, please post them with reference ranges so we can better assess your current status.
Why are you hoping to get off the anti-thyroid med? That's, most likely, what's keeping your levels stable and if you go off the med, there's a good chance you'll become hyper again.
To answer to your question specifically, yes, you will always have Graves Disease; yes, there's always a chance for relapse; and yes, periodically, you should get the tests I mentioned above, which are Free T3, Free T4 and TSH, to make sure your levels are staying within normal ranges.
I'm currently getting labs done every 3-6 months and have been stable for the last 6-9 months. I'm forgetful to take my medicine sometimes till like 9 or 10pm.
I have been off the meds since 2010. The key is to make sure the antibodies that cause the disease are GONE. That would be TSI and TRab (TSH receptor abs). IF those are gone, then you no longer have Graves.
My son has been off meds since 2006 ---- and only needed the drug for 4 years before TRab/TSI went Negative.
The key to staying in remission is AVOID HIGH IODINE. And that means NO seaweed,no iodine vitamins, no iodized salt, no iodine medications or contrast dyes. You also want to make sure your TSH levels stay under 2.0 since heavy TSH receptor activity can stir up the TRab again.
Good luck to you! But don't stop the meds UNTIL your TRab are below 0.9 and your TSI is under 90%.
I actually don't think that my antibodies have been measured yet or in awhile to be honest. Also, I was diagnosed in early 2014, so it may be still early days.
If you haven't had any antibodies measured, then you don't even know if you have Graves Disease... You have to have Thyroid Stimulating Immunoglobulins (TSI) tested in order to confirm Graves Disease... otherwise, you could be in a hyper phase of Hashimoto's and may go back to normal or hypo on your own.
You must insist on antibody tests to find out what you actually have. TSI for Graves Disease and Thyroid Peroxidase Antibodies (TPOab) and Thyroglobulin Antibodies (TgAb) to diagnose Hashimoto's... Must have all three or your diagnosis may be incorrect.
I was diagnosed with Graves' disease at the age of 12 and drank (apparently it's a pill now) Radioactive Iodine.
I have not had any problems since then with taking synthroid except when they fluctuated when I was pregnant.
A lot of people hear "radioactive" and freak out but the iodine goes straight to the thyroid so there are no residual effects of radioactivity.
I am 45 years old and pretty sure I would have noticed by now.