Whirpool gas dryer - starts but wont stay running
 

I've got a Whirlpool gas dryer (Model GGW9878LWW) that wont' stay
running.

When I press the start button, the tumbler starts spinning, and I can
hear the flames ignite (the clothes do get dry too). When I release
the start button, everything stops. I need to put duct tape over the
button for the clothes to dry.

I can hear a relay engage when I press the button as well.
The dryer door switch is working fine. I can make the dryer start/stop
by pressing/releasing this.

Is this a common problem with Whirlpool dryers? It's only 5-6 years
old.

I would like to see if I can fix this myself, I'm fairly handly with
home repairs.

thanks for any help.