Maybe one of those stand alone bobbin winders might be in order? I'm not really sure how to slow down the auto winders. When foot controlled it was easy. I've never used a stand alone, but I've heard many compliments here, particularly the 2nd generation ones.

edited to add: I do have my Singer 404 vintage machine set up all the time, I'm thinking if I do something with the stretchy thread, that would be the place to wind the bobbin. Why buy a 30 dollar single use machine when I have a multiple use 30 dollar machine :)

I wound another bobbin about half full with nylon thread, just as a test. My machine is singing along just fine and so far, no bobbin issues. I think we've discovered the problem: operator error. LOL –– Thank you all so much for your help!

I use to overfill my bobbins on my Viking in the 70's and one side of the metal bobbin would pop off. But with the new machines overfilling does not appear to be possible.

I've had this happen with a plastic bobbin for my Viking, but I assumed that it was an old one from the early 1980's and that I filled it too full.

My Granddaughter was complaining to me about her bobbins breaking I had never had this happen so didn't know what to tell her now I know too

Just recently I found 2 Janome bobbins broken in the bobbin box, one was the blue one, the other clear, both had been filled with cotton thread at different times and were probably 2 years old. In each case the a side had popped off, had been used on different machines & had been put away in different bobbin boxes. A mystery to me.

I have found that if you slow down when filling a plastic bobbin with the clear thread and only fill it 1/2 full it seems to help. I have a Pfaff Passport 2.0, I broke a bobbin last time I used the clear thread, it got stuck on the bobbin winder.
Sharon in Texas

Yes, my Janome bobbin broke also, just winding regularly with 50 weight thread. The end just popped off.

I have a Janome 8900qcp and have not had any problems with bobbins breaking and I have used my machine a lot both for stitching and FMQ.
When you fill your bobbins, especially with the clear thread, try using the on/off switch rather than the foot pedal to run your machine and set the speed on slow. The on/off switch is a more even speed than using your foot so the bobbin will fill more evenly. You don't have to worry about when it comes to the full point because the machine won't let the bobbin overfill. Just hit the off button when the bobbin stops going around.

I broke one once winding it too tightly/fat. Other than that have had no problems with the Janome bobbins. They are expensive too especially the colored ones. No fun losing one.