I have a Juki on a grace frame and it works fine with cotton thread .. I use Connecting Threads large cones with a 14 needle.
A few tips to check .. make sure the machine is threaded correctly while the pressure foot is up.
...make sure the bobbin is in correctly
...make sure the pressure foot is down during the quilting
...always bring the bobbin thread up top and hold both threads when beginning to quilt (you can knot and weave them in later)
Hope some of this helps .. I'm sure more experienced folks will come along soon to give you better help.
Good luck .. I'm sure it's something very simple ..:D