I have a Kenmore Elite electric dryer . Model 110.62994101 the will not stay running after the start button is released. I am suspecting that a relay on a main board is bad. Or could there be a less expensive repair solution.

On older dryers, the latch circuit is made through the centrifucal switch on the motor, if your dryer shows a relay, I would note the wiring drawing. If the drawing depicts that that relay is for the latch circuit, then it is possible that it is bad.

Is there anything else wired in with the hold circuit?