Must be a bad chip. I put it on a breadboard and found that the problem is not that the chip doesn't reset -- it actually does respond to pulling RESET low. The problem is that it does not restart after a reset.
To eliminate the bootloader as a variable, I burned the Blink sketch into the chip using my programmer (i.e. no bootloader).
Initiating a restart by either 1) toggling the benchtop PSU, or 2) pulling/inserting the banana plug from the PSU to the breadboard allows the Blink sketch to restart.
But if I press the Omron tactile switch (RESET to GND) on the breadboard, then Blink stops and does not restart. Likewise, if I pull and reinsert the VCC or GND jumper wire in the breadboard rails then Blink stops and does not restart. (There is a 10K pullup on RESET).
The chip must be overly sensitive to noise on VCC, GND, or RESET. I have a 47uF across the breadboard rails, and 0.1uF's between VCC and GND, between AVCC and AGND, and between AREF and GND. I also have a signal diode between VCC and RESET to clamp high voltage spikes.
A different chip mounted to the same breadboard config works as expected, i.e., no problems.
Gonna toss the chip.
Jim