I have two power banks. Both in seemingly good condition. One is 16750mAh, DC 5V/4.5A max. The other is 10000mAh, DC5V/2.1A max. I've built several very small projects with a Nano and using various sensors, and RTCs. I built two clocks, one with a LCD and the other with a 4-digit display. Whenever I plug my Nano based projects into either power bank it will run for a short period and then the power bank shuts down. These projects cannot be drawing much current. Can they? Any ideas why both would shut down and across multiple projects?
I'm guessing that the power banks are auto powering off because the nano is drawing so little current that they perceive that there's nothing connected to them.
Yes, remember that powerbanks are designed to recharge the battery of another device, like your phone, not to power your Arduino projects. When the "charging current" is below a certain level, the powerbank figures no charging is needed, and it shuts down to preserve its own battery. There are ways to periodically sink some extra current to prevent the shutdown, but in the end you are still wasting powerbank power just keeping it turned on. So they are mainly useful for projects that draw a lot of current in the first place.