It's easy to quit trying different things when you take health into your own hands, especially when medicine is usually in the business of management rather than cures. Sometimes there are no cures for the problems we do not completely understand or the problems are not responding well to a treatment, whether evidence based or not.
With that said, Hashimoto's response to Iodine is not a guarantee to achieve any expected result. The autoimmunity of Hashimoto's only explains that lymphocytes are attacking the thyroid, but any conclusive explanation as to why lymphocytes are attacking is difficult to diagnose without specialized testing and comprehensive MD. Sometimes it may be due to lack of iodine, but from what I gather it could be a malformation of the thyroid hormone, malfunctioning immune system, infection, toxicity, allergy (autoimmunity?), or nutritional imbalance.
I personally do not have Hashimoto's, but take amino acid L-Tyrosine, Nascent Iodine, and Selenium on a regular basis with whole fresh fruits usually.
Iodine 400mcg 1 time in the AM or after waking.
L-Tyrosine 500mg 1-3 times daily during stress (I work in a hospital's ICU, it works great for stress).
Selenium (ionic) 50mcg with the Iodine 1 time daily.
I also take a liquid multivitamin that contains Iodine and selenium already with Vitamins A, Bs, C, D, and E, various minerals like Chromium, and a few other herbs.
The biggest change to my diet is avoiding certain foods and food additives that I think may help you as well, if you already have not started avoiding certain foods or additives.
Some have claimed that avoiding Gluten and/or Casein will reduce the antithyroid peroxidase antibodies. Have you tired that?
I personally avoid partially hydrogenated and hydrogenated oils regardless of source, but will sometimes eat them, rarely. Genetically-Modified foods, pesticides, growth hormones, and the like are everywhere and consider them toxins. Corn is a big one, almost all of corn on the market is Genetically-Modified and added to practically everything, ie. High Fructose Cord Syrup (HFCS). Did I mention that 1/2 the HFCS tested positive for mercury contamination? Did I also mention that it was HFCS tested, not where the HFCS ended up? Food for thought.
According to the bottom reference (please give it a read), some of the possible triggers for Hashimoto's are:
-> Viral, bacterial or Candida infections as a trigger or as a direct cause;
-> Ongoing stress, sufficient to cause adrenal insufficiency that hampers conversion of T4 to T3 and weakens the body’s immune defenses;
-> Pregnancy, which up-regulates the immune system;
-> Trauma, such as surgery or an accident;
-> Nutrient deficiencies, in particular of iodine and/or selenium; and
-> Food borne bacteria, most notably Yersinia enterocolitica, though this is more common outside the U.S. (Shomon, 2001).
SIDE NOTE: Forgot to mention, I take SSKI sometimes as well. When I went on "vacation" and stopped taking any iodine, I got sick on my flights back home. The full story involves me not sleeping the night before, expecting to sleep when I get home. One of my flights was cancelled and all planes grounded during a snow storm for 12 hours. Staying awake at an airport, total of 2 days, screwed up my system and I ended up with a sore, clogged throad, and a deep, hoarse voice for a week. Other typical cold symptoms were few, if any.