It's for a bird bath. I want it to run all day. I didn't want to have to plug it in to a wall outlet. Spent more than planned but I got a 12w power bank and it seems to be working. So far.More likely your powerbank doesn't like powering motors... If its 5000mAh it should run that motor for 5 hours (assuming its charged). But motors are finiky things, they take a lot of current to start and are electrically noisy, both of whch could upset the protection circuitry in the powerbank.
How long do you want the pump to run for?