Hi there and welcome!
The best explanation is that the relay (a switch) on the lower circuit board is stuck in the "on" position. The top controller cuts signal to that switch to tell it to go to the "off" position but if the switch is stuck in the "on" position, the switch will just keep letting the power flow to the heating element until the overheat safety switch cuts power off at like 305F degrees or so. Once it cools enough that switch will close back down and you will enter the same cycle becuase the relay is still suck in "on".
If you were more crafty than I with electrical components and could switch out that relay on that circuit board you would likely fix your situation. I think I've only ever seen 1-2 guys come through here that have done that but didn't really post about it much so not a lot of info to easily figure that out unless you deal with circuit boards and hardware like that a lot.
Your alternative is to do the simple rewire to bypass all the MES electronics and use a PID controller to run your smoker.
The Auber PID controllers run like $160 which would cause most people to think "that's almost as much as buying a new smoker" BUT, doing this is not turning your MES into an electric smoker that would cost over $1,000 brand new.
I always say its like turning a golf cart into a Ferrari! Your MES would look the same but perform a bajillion times better where it hits and holds the temps dead on or within 1-3 degrees.
Also when doing this rewire, if you switch out a few cheap wire connectors to ones that wont corrode away like the factory MES ones do, then you will have a smoker that you can keep running until a tornado hits it lol.
All of us MES-PID guys seem to wonder "why did I wait so long" after we've made the switch. I haven't heard anyone ever be disappointed with doing it :D
Here is the simple rewire guide for using being able to use your MES with a PID and avoid issues like this from now on :D
Lately I've seen a number of posts about guys wanting to rewire their MES. I had wanted to post a quick and simple guide for those out there that are curious or those that simply need to rewire but need a little assistance. Well here goes. Disclaimer: When messing with electrical equipment...
www.smokingmeatforums.com
I hope this info helps, ask any questions you have.