Mechanism. The thyroid has 2 months of thyroid hormones stored inside it. When it gets inflamed (thyroidtis), it can't hold on to the thyroid hormones and the hormones leak out into the blood stream. That's why you have high level at the beginning. Once all the hormone is leaked out, there is no hormones left and the body has to make the hormone again which is why you become low.
Great question. I looked up pathophysiology of hashimotos and it states that its poorly understood. Maybe a pathologist can help answering this question. My guess would be the thyroid gland tries to build more hormones to compensate for the loss. At first it wins the battle, but eventualy theres too many antibodies so it gets "burnt out".