Look around for cold solder joints at the usual places:
=On the Duo, there is the small PCB board that the power supply end plugs into. If I were having power issues, I would just touch up everything on that tiny board with new solder. Suck off the old, add new (reflow), piece of cake!
=Reseat the cable that connects to the motherboard from this tiny board.
=Lastly, I would reflow each of the 7805's legs. They (x2) generate a lot of heat, and I would think the legs could have fractured the solder over the years. After all this I would see if it is any different and then pull the meter out.
Once, I was refurbishing a first model Playstation (the one with the built in composite on the back) and it had a cold solder joint at the power pin that was preventing it from even powering up. Usually the fault is itermittent, like you describe, but this was completelty stone dead. It took 5 minutes to get it up and running (and a donor PS One drive to make it functional).
I hope this helps, it is really a quick job once you have everything disassembled. Not hard at all, even if all you have is a non-temperature controlled $7 wand
I haven't had this particular issue yet, but I hope these tips get you going again.