Try setting your tensions according to this Jamie Wallen video:
http://www.youtube.com/watch?v=Q1mRhcquZTM . When you have skipped stitches in just one direction like this, my best guess is the tension settings. The stress put on the thread changes with changes in direction, so your tension settings may be fine for all but the one direction. Of course, you need a tension setting that works for all directions.
Also, I would try a stronger thread (such as Auriful 40wt) and definitely a larger needle (at least size 16). Frame quilting puts different stresses on the needle and thread than fmq in place. How taut or loose is your quilt sandwich? A common mistake is to make the quilt too tight on the frame; rule-of-thumb is to be able to grab a finger pushed up from underneath the quilt. Also, different machines prefer the quilt at a different distance from the base. Mine likes the quilt riding on the base (but not dragging from the takeup roll); others prefer the quilt to ride 1/4" above the base.
I would also recommend making just one change at a time and then test after that change so you know immediately if something has a strong positive effect (or if you have introduced a new problem).