Loop Back Test - Sticky?

What does it mean if the loopback test works without connecting RST to GND?
Like many other people, I have a board (Nano 3.0) which suddenly ceased to work. When I first received it, it had no bootloader so I burnt one using a Mega2560 without any problems. Over the course of a couple days, I used the Nano to test a Nokia LCD screen, some temperature sensors, and a few other things all problem-free... then one day, when I plugged it in to try something else, and it seemed have to lost it's bootloader. I've tried to reburn the bootloader unsuccessfully several times, getting the same avrdude verification error which seems to indicate fried flash memory.
The loopback test works and everything sent gets echoed back, even when RST is not connected to GND, which gives me the impression the reset button is stuck on or shorted somehow... I've examined the board with a magnifier and do not see any shorts.
Anything else I should try?