bear, smoke a cigar and save your ash in a small bowl. Sparingly spit in the ash, and mix it up until it is a dry gritty consistency. Then simply apply the mixture to your weak spot inside your bowl, similar to the way you would use a trial to spread mortar.
You will be amazed at how the cigar ash dries to a concrete like consistency, especially so if you are careful not to get the mixture too soupy.
If you mix it up just right, it will resist chipping and coming back out of your pipe. Once a cake begins to build around the area, it will just keep getting more resilient.
I always do this with a new cob to protect the bottom of the bowl, and I never have problems with the bottoms of my cobs burning out.