I have thyroid problems too and for a while "they" thought I had Hashimoto's disease, though in the long run I did not. I did though lose two babies early on and did not recieve testing until I began seeing a reproductive endocrinologist. He found that I had a low level of progesterone and put me on a high dose of Prometrium as soon as I got pregnant the third time. (Prometrium is a soft pill which I inserted vaginally. Very messy but worth it to carry the baby full term.) I got several progesterone shots too.
I did not see the RE after delivering my first son and with each pregnancy after that I was on the phone immediately, within minutes, of getting the little double lines, insisting on a Prometrium Rx from my family physician. I usually got the run around, because at this clinic you have to go talk to a nurse first, but I kept at it. I would usually have to leave a message with my doctor's nurse, who knew my history better than the person answering the phone, and could get a Rx within the day. If I were you I'd keep after them. Or go see someone else entirely.