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You're welcome to paint it but it'll never be the same. My minivan had that problem on the hood and I stripped it bare down to the primer before repainting it because it kept shedding chunks of paint. For some reason, the color coat stopped adhering to the primer. It sorta looks the same with yours but I can't tell for sure.

Was that bumper repainted at anytime? It looks like a white color coat instead of primer underneath that dark shade of paint....

 

The bumper wasn't painted properly. The paint never made a bond to the actual bumper.

Your paint should still be under warranty from the body shop it was worked on; if they're reputable. The bumper needs to be repainted again. Sorry to be the barer of bad news.

 

Wow, that shop sucked. It should be their job to fix no matter what the cause because of their poor prep job

 

i agree with these guys. a few years ago, i purchased an after market bumper and took it to a body shop to have installed and they did, what seemed like, a great job. not even a week after i got my car, a rock must have hit the bumper and the paint cracked and started peeling. turned out the shop never primed the bumper and the cracking resulted (similar to your picture). the paint should never peel off like that.