I've measured the power consumption to know if the boot problems I was having had anything to do with the power consumption.
The problem I'm having happens only on power on so I started measuring the current on boot, the current starts at around 100 mA and has a peak at around 360 mA. This is far below the max output of the power bank at 1000 mA.
For comparison I also measured the current draw when it is idle and powering motors. In the idle state the current stays around 330 mA. When the motors start there is little peak and then it goes to about 600 mA.
If you compare the current draw you would expect that the boot wouldn't draw too much current. It could be that there is a really quick peak current that my multimeter is too slow to pick up and sends the electronics in some sort of reboot cycle, but that is just a guess.