Electric Power Mystery

I own an all stock 2006 sport edition v6 4Runner.
I bought a power station from Anker called c1000. When I try to charge it with the car port it starts drawing power from the rear DC port and increases incrementally say 15, 35, 50, 65, 85 watts. I know this because the power station displays the measurement. However, as soon as it reaches anything around 85 (usually takes a few seconds), it cuts off power and goes back to 0 and the incremental charging restarts.

Does the truck have a mechanism that cuts off power when it reaches too hush of a wattage? Has anyone experienced something like this before?
What are safe proper ways I could charge my power station working around the car port?