I know its a late response but I have a solution when using the ht4928s chip.
I use a 50 Ohms resistor to generate some load the keep the "powerbank" chip enabled. But it is switched on and off by a transistor (PN2222). The transistor is controlled by the arduino. After some experimentation I found out the load only has to be enabled for 0.01 seconds every 3 seconds to keep the "powerbank" on. Effectively this will only 0.333 mAh.
It's not a perfect solution but for most applications it is acceptable.