Thoughts:
1. It may be the fabric.
2. It might the be the presser foot pressure
3. The tensions discs might need cleaning. I was taught always to snip the thread at the reel and pull it through from the needle end when changing thread - pulling thread backwards through the tension discs can sometimes snag it and leave little threads stuck there, interfering with the closing mechanism.
4. Daft suggestion - Have you made sure the foot is down? I teach sewing and machine techniques and the number of souls, who, every.single.week forget to put the foot down - is unbelievable!
5. Have you checked the bobbin case and hook area? little bits of fluff/thread can cause all sort of issues.
6. Oh yes, thread.......My old Bernina will sew with anything. However, my new Bernina B540 is a picky toad, likes Mettler, Glide, doesn't like Gutterman at all!
7. Which Bernina do you have?
Sorry if this all sounds like stuff you have done or heard before!