Sometimes it just helps to turn the needle slightly to the right. Also the tension spring can get a grove worn in it and need to be replaced. I'm pretty positive we're not supposed to oil the tension or the thread on a Handi Quilter. You can use a silicone spray on the thread, but only if it's an ornery thread, and very sparingly. Black thread is more ornery than lighter colored threads, because it has been dyed more than once. The arm that the thread goes under, just after it comes out of the tension, can be twisted slightly to hold the thread from jumping out of the tension.
Good Luck to You!