"What do you think would cause a vintage singer 66 to go in and out of tension? "
There could be different reasons...one thought that came to my mind was that maybe something got caught between the tension disks. Another thought is ...you have make sure that you have the presser foot "up" when you are threading your the top part of the machine. Don't put the presser foot down until you have done everything but put the thread through the needle. If the presser foot is down when you put the thread through the tension disks, then the thread does not go into the tension disks correctly.
I would also check the bobbin case to make sure that there weren't any burrs on it and that the bobbin tension was okay.