If it has been a while since the needle has been changed, doing so may be helpful. Also be sure to use a sharp needle that will more easily penetrate the zipper tape.
Be sure that you are actually lowering the presser foot before stitching (this most likely isn't the case--just a thought).
Most machines also have a presser foot pressure adjustment that can be loosened or tightened to accommodate different thickness of fabric and the amount of pressure applied by the zipper foot on the fabric and the feed dogs. Experimenting with that pressure adjustment may be helpful.
Some bobbin cases also have a finger extension with a hole through it. If you are experiencing issues with bobbin tension, sometimes threading the bobbin thread through that finger will help even out bobbin tension.
Using lighter weight thread will also affect the resulting thread tension. If the bobbin case is wound with light weight thread, the bobbin tension will not operate the same as it would with standard weight thread. Light weight thread in the bobbin will cause looser tension, but heavier thread will cause a tighter tension.
Technicians use a standard weight thread to test tension on a machine, but if you use a different weight thread, then your results most likely will not be the same.
Bobbin Tension How and Why Tension is Adjusted
How can properly adjust my tension
Understanding Thread Tension Threads
Most tension adjustments can be accomplished via the upper tension. However, there are times when the bobbin needs to be adjusted. Sewists are frequently nervous about adjusting bobbin tension. It is important to mark with permanent marker where the skrew-slot is positioned on the bobbin case BEFORE attempting any adjustments (at least if you need to return it to the original setting, you'll know where it was). Make only 1/8 turn adjustments at a time and re-test. (Righty-tighty, Lefty-loosey!) Sewists who frequently use different weight threads in their machine will often have an extra bobbin case that is set up specifically for that thread weight so they don't have to manipulate the bobbin case every time a thread is changed.