Here's a few ideas;
1- The paint could be from a bad batch. This is rare but it does happen. Most manufactures will deny this and it is difficult or impossible to prove.
If there is a problem with the actual paint it could cause loss of adhesion or produce a brittle finish.
2- Not enough applied paint or wrong type of paint. First, it is really hard to get good coverage and a thick coat on the edges. It takes several coats carefully applied.
The type of finish also effects the longevity and toughness. There are many types of paints/finishes available.
3- Lack of primer or not enough primer. Priming is one of the most important steps and easy to overlook. Typically- a heavy coat of sandable primer is applied, allowed to dry and sanded ultra smooth, then another coat is applied, then the finish coats. The type of primer and amount depends on many things but this could explain your problems.
One way to check for primer is to look at the wood under a peeled area and the back of the peeled film of paint. Either the wood or back of the paint film should show the primer as a white layer, white is a typical primer color.
If no primer was used then this is most likely the problem.
Each one of these alone can cause problems similar to what you're experiencing. The only way to truly fix this it to sand off all that is loose, includes lightly sanding all surfaces looking for loose paint. Now remove all dust and apply primer. Then repaint everything. In my opinion this is the only way to fix this once and for all.