BulldogLowell:
building on @krupski advice, you could try simply adding a capacitor across VIN and ground on your Nano. Something substantial, like a 47uF electrolytic. That may help with a power ripple. If it doesn't solve the problem, then that narrows the problem down to perhaps the power regulator on the board.It's a 50 cent part.
Good idea. And it's super simple to try since the cap leads will simply plug into the Arduino header.
A small note: Be sure the capacitor is installed the right direction. A 47 uF or so cap is most certainly polarized and will not work (and maybe even explode) if inserted backwards.