The board is bad. I know you've had it replaced twice already, but it's bad again. Something else is causing it to fail, don't really know what, may be the sensor or one of the thermostats. If you replace the board, it will most likely fail again. It's pretty impossible to have 2 or 3 defective boards in a row. If you want to fight it, Sears should take care of it. It might be difficult to convince them, but in the end I think they will take care of it.
If you'd rather get a new dryer, keep in mind that this one, as most Sears dryers, was made by Whirlpool. Sears does not manufacture any appliances. Whirlpool generally makes pretty good dryers, you just got "lucky"
. I bet if you get the same exact model dryer again, you won't have any problems. On a different note, I would never buy an appliance from Sears. Their warranty is a lot worse than what the actual manufacturer offers (Sears always tries to push their extended warranty for extra $$$) and as far as service, it's almost always better to call a local repair company than Sears, in my opinion (I know you had no choice, because of warranty).
Hope this helps.