How do you repair erosion in the joint between the inground swimming pool and the swimming deck?

Try to shove a very dry, very weak, sand cement mix down there about 25 to 1 should help stabilize it enough to top it from getting worse. I think the better course would be to remove all the old caulking, clean out all loose materials, install the foam insulator/depth material ( usually sold in rolls - can be precut to varing depths) , then pour in ( once mixed properly) the Deck-o-seal caulking. Follow the directions on the product ( which can be found at most pool stores) explicitly - in other Words do not vary on the mfgr's instructions. If the mfgr calls for mixing the two products a & b for ten minutes - that does not mean 8 or 9 minutes. The key to a successful job to completion is proper perperation. This is not going to be a rush job so plan ahead. Do not start the job late in the afternoon or when it is going to rain. Best to do the job when temps will not exceed 75 or lows of below 50. When purchasing the product ask lots of questions about the product, preperation, cure time, working time etc.