See Replace ATMEGA328P-AU chips - Avrdude, stk500, Bootloader issues - Arduino Forum
He reports that the problem is caused by a bad firmware on his USBAsp.
It may be that there's a new batch of USBAsps going around that has firmware with a fatal bug going around (this would explain why we're only now getting reports like that). If you can confirm f/w upgrade fixes it, complain to seller and try to make them aware so that the problem reports get propagated up the supply chain...
Boards are probably recoverable with HVSP, but HVSP requires modifying the board because of the probably unnecessary diode from reset to vcc.