Try pulling out several feet of thread slowly from the bobbin case, and see if you can find where it gets tight. Then put it in the machine and do the same thing - running it through the needle hole.
Then try giving it a quick pull and see if you can get it to lock up.
I have run into the problem when the bobbins didn't fit quite right - they were a bit loose and if the machine gave a quicker jerk, the bobbin would spin inside the case and then the thread would wrap around and then get underneath itself -and then tighten up and snap.
Also - check how you are winding the thread on the bobbin. I've run into a lot of bobbins (coming with old machines) that were wound with poor tension, and then the thread gets underneath lower levels and will not pull off correctly - and gets tight and breaks. I've had some so bad I had to cut the threads off the bobbin.
Always makes me wonder if some machines got relegated to the closet because the owner didn't know how to wind a bobbin and kept breaking thread.