Hi, when I use old reels of cotton they often have a nick on the side to hold the loose thread, and when sewing the thread gets caught in the nick and pulls tight and breaks. I use an emery board to obliterate the nick or else reverse the cotton reel so it unwinds from the top instead of the bottom and have success. So maybe if all the other cures fail, go back as far as the cotton reel and make sure it isn't causing the problem.
good luck!