Never fear, the culprit is probably just your Take-Up Finger.
Let's break this down:
When a sewing machine is threaded, it is easy to forget the Take-Up Finger.
The Take-Up Finger is a lever that lifts and lowers the thread with each stitch.
Depending on your machine, the Take-Up Finger will be in the front or side above the tension control.
Check out some examples at the end of the article.
The Take-Up Finger is needed to pull the upper thread around the bobbin and back to the surface. Without it, the thread is taut and is unable to give.
Next time the Three Stitch Problem turns up, take a look at your Take-Up Finger. Rethreading the machine may save you a lot of sewing anguish.