The brick used to make most consumer kilns is fragile. It is made by mixing refractory materials with wood pulp and then firing it to burn out the wood pulp. Air is the best insulator so all the little pockets left behind help your kiln retain heat and make the kiln much lighter.
Unfortunately this process weakens the breaking strength of the brick so odds are you will occasionally chip your brick. This normally happens when you are loading shelves and ware into your kiln.
Most chips and dings will not affect the performance of your brick. The areas that will need attention are your lid, element grooves and slabs (kiln floor). It is very difficult to patch brick in areas where gravity is working against you such as sidewalls and the underside of your lid.
Most manufacturers coat their lids with refractory cement designed to seal the brick so bits of brick dust do not fall into your ware during the firing. Sometimes trying to patch the underside of your kiln can actually create more problems if the patch does not hold. Since many lids are coated on both sides it is often possible to remove the lid hardware and flip the lid over.
The element grooves are designed to hold the element in place so it does not want to droop down when the element heats up and softens. If you break out an element groove usually the best thing to do is go ahead and replace the brick. Often times kiln owners will postpone brick replacement until they are ready to replace their elements. A good way to hold the element in during this period is to form a little fence using element pins. This is definitely a temporary fix but it can usually get you by until you are ready to replace elements.
The floor of your kiln can get worn of time. Small bits of melted glaze or glass may need to be chipped out leaving chunks missing that can affect the stability of your shelf posts. This is one area where patching can be very effective. Most kiln manufactures make a kiln patch using a binder with brick dust. Just use a spackling knife to apply the patch and let it dry before you fire the kiln.
The process recommended for replacing brick will vary between manufacturers. The brick will also vary since most manufacturers groove and cut them differently. You will also notice that brick types within the same model will vary. Check with your supplier or manufacturer to verify the brick you will need.