This sounds like an electrical connect problem, possibly with the cord/pedal. I had a similar problem with a serger and once I got a new generic pedal it works great. If its a consistent stop and go, it might be in the computer program. Can you contact Baby Lock for support via the internet? I have an Esante, one of the first computerized machines by them that has worked great for 18 years, except for the parts that I wore out!

Have you called the customer service number? Sometimes they will have a quick solution.