Serial communication failure when using power supply

This tells me the problem is coming from the PC, but I don't know how to prevent the resets on the Arduino side.

I see this as a big problem in my particular application. I hope a solution comes soon.

Sounds to me like your PC has something in it that is scanning for unconnected comm ports, such that as long as the comm port is opened and assigned to an application like your processing program then all is well. But when you quit the app and the comm port is released something is scanning for it by opening it and then closing it at a periodic rate. Do you have any bluetooth drivers active, or something like that, that would be searching for comm ports?

Lefty