That oldtimer probably sanded the heck out of it and prepped it wrong. Plastic bumpers just need a good flex additive and proper scuffing, skipping it is asking for trouble but a month is still fast for failure.
Honestly yeah, that "month is still fast for failure" part hits hard. I had a buddy who prepped his Civic's front bumper the same way, thought he did everything right with the flex additive and all, and it still started flaking around three weeks in. Turned out he didn't let the primer cure long enough before paint. That oldtimer might've rushed the drying times too, happens more than people admit.
Did I crash my Camry into a shopping cart last year because I skipped flex additive too? Probably. But in my defense, I also thought I knew better than the guy at the auto parts store.