I have a Powercore II 20,000 that I thought was defective this week. The first time, I charged it with a 1A wall charger and it was complete in maybe 20 hours or so. No problems.
The second time I tried again with a 1A Apple charger and the lights would blink for a few minutes to indicate charging, but then the lights stopped. (I have confirmed the Apple charger is working because I continue to use it every night to charge my phone)
A few days later, I used two 2.4A chargers and now the Powercore successfully charged.
Is there some issues with 1A charging?