OK, I got some help at the local stove store. The thing I burned the hole through is a baffle. Its fucntion is to keep the hot coal gases in the stove longer, instead of going straight up the stove pipe, and increasing the burn time by up to 30%. They have a finite live span, as is evident by the gaping hole in mine. Not loading the coal right up to this baffle will help prolong its life.
It cost me $65.