Rather unexpectedly, we found the solution, while passing time at the airport in Ottawa, Ontario, Canada earlier this month (March 10). I noticed one of those "10 Minute Manicure" kiosks in the terminal, and I convinced ny wife to have a manicure. As I was chatting with the manicurist, I picked up a glass (crystal? - made in Czech Republic) nail file, which ws obviously **much** better than the metal one that I had been using, having a finer, more uniform abrasive surface, etc. We bought a few ($10 ea.; available cheaper, however), and immediately I noticed that my nails no longer chip or flake!
As I was looking at it, the manicurist said that it helps "bond" the ends of the nails, which may be true. She also said that thay last virtually a lifetime (years), and are hygienic and easy to clean / sterilize, ... Certainly, they were worth every penny! One precautionary note - these can file your nails doem very quickly - use sparingly, just to keep your nails smooth and trimmed, and to catch / smooth any small nicks, fissures, damage, etc. (as they arise). :-)