Typically in the body shop once the clear-coat is broken, refinishing is required. If the clearcoat is broken and it is very small ( stone chip size) you can perform a minor touch-up.
With the clear-coat the size of a silver dollar is peeling, this suggest clear-coat delamination and most likely the problem with continue. If the car was repainted at some point this may also suggest an adhesion problem with the clear-coat. The cause could be numerous items from an incomplete cleaning prior to refinishing to incomplete mixing of the refinish materials, to improper refinish application techniques( waiting to long to apply the clear-coat after the base coat was applied)
There are also numerous other issues with attempting to touch-up clear coat. Each paint vendor ( Dupont, Spies, PPG, etc.) has their own products and formulas. Matching the hue or tint of the clear is almost impossible, hence the reason the auto collision industry typically does not attempt to touch-up just one area of a panel, the entire panel is clear-coated