Hi,
Firstly, you need to mak sure the input power bigger than output power considering the efficiency. (Pin=Vin*Vin/4/R)
Secondly, there is a OCV detecting time around 300ms when the ADP5090 can't convert power to output to suppot this several mA load.
so you can use bigger capacitor or use a fixed voltage power source at output to monitor the current flowing into.