Apparently I'm not the only one facing the frightening brick mode on my Peak.
On the B2G mailing list another enthusiast found himself in the same situation. Hopefully, Jan Jongboom gave a hint in the right direction. According to him, computer USB ports don't deliver enough power to satisfy recent phone needs. He reckons a USB charger plugged right on your wall outlets should do a better job to give an electroshock to devices.
I'll definitely have a go, because it's getting quite dramatic to have to practice an emergency reanimation on Peaky every time he sleeps for a bit too long in my drawer.