Hard to tell from the picture, but it certainly looks like a poor preparation process to me or lack of any plastic adhesive promotor /primer.
It could suggest that the coloured base coat and lacquer have peeled together, revealing
the black area seen in the picture.
This is the actual raw colour of the moulded plastic bumper cover itself.
The bumper cover has not been prepped correctly prior to paint, or the plastic primer adhesive coat has been completely missed in the process.
The plastic primer coat bonds tightly to the plastic cover and then it can be primed prior base coat & lacquer.
With out the plastic adhesive promotor applied first, when the plastic bumper cover flexes, the paint just cracks then flakes off due to the lack of adhesion between each paint application.
Effectively then the base coat & lacquer etc is just sitting on the surface of the plastic bumper cover and not boded to the surface.
As it is unclear if it is just a few bad contaminated areas under the paint or indeed the whole bumper that is affected, then the cover should be removed and completely sanded / stripped back.
Otherwise a local repair could see you end up chasing the problem again at a later date in time.