Real thyroid conditions are Autoimmune Diseases and they never go away. Without daily treatment of some type, Hypothyroid and Hyperthyroid, etc. patients can/will die. Going on and off of thyroid medication will put the thyroid in jeopardy and will put the thyroid in remission, can cause cancer, and/or complete thyroid failure and removal of the gland. (Edited* in comment below- no room here).
If your thyroid is level, then that means the medication is working and you haven't gotten worse; that means you are on the correct dose for you for now. Hopefully, you will be lucky and it will never change, but usually after a few years it does. *Look up Mary Sharmon(?) on http://www.about.com and look under hypothyroid. There is tons of information and points that you can research from. The actual articles are approved by a board of top physicians before they're allowed to be shown, so they are reliable. I would avoid the commentary, b/c it has been reported that a lot of it is false and they do not go through to weed that information out. They also offer natural thyroid remedies and replacements if you are interested in that.
Additionally I would look it up and search official sites on your thyroid condition, it may help you become more aware of the catastrophes you will face by avoiding the medication. If you choose more natural remedies or the medication you are on, please make sure you are getting your blood checked regularly still, to make sure it is working and you are on the correct dose.
My apologies for being blunt, but that is a condition too serious not to be informative about. Best Wishes in your journey.