Buffing isn't really necessary unless you're removing flakes. Also, over-zealous buffing can lead to thinning of the nail and you don't want that!
The most likely culprit for the peeling is layers are too thick? Try to keep your layers thin and only do as many as are absolutely necessary. The more layers - the more quickly it will peel. Also, don't soak your nails or shower right before you apply polish. The nails are porous and absorb water so once they are dry they shrink back, which can cause chipping and peeling.
Make sure there are no oils on the nails before you start, so after you've filed and prepped, make sure you remove all oils again with polish remover or alcohol ('squeak' them!). Then apply base coat, colour and top. Make sure you cap top of th the free edge of the nail with colour and top coat, this should prevent tip wear happening as quickly. Also try and avoid getting any polish on the eponychium (what a lot people mistake for cuticle!) and side walls - anything that causes ridges or bumps can lead to peelage or the temptation to pick.
The other thing that can make polish peel is cuticle on the nail plate. Really I don't feel happy to recommend anything for that though except getting a professional mani.
Hopefully some of that will be helpful.
