Kenmore dryer won't keep running after release button

I have a Kenmore electric drier with a push-button start. After I set the time, I push the button and the drier will start normally, but won’t keep running if I release the spring-loaded push button. Right now I’m using it by taping the button down into the start position. It’s otherwise ok, dries well, etc.
I replaced the button and it still does it. Is there a bad relay somewhere? How can I fix this?

sounds like motor is problem