Me too. The turntable would run for a few seconds, then the battery would shut down. This happened on two different battery packs. Turns out the problem was that the turntable draws WAY less than the its 2 watt rating which apparently isn’t enough to keep the battery pack interested.
As an experiment, I hacked a USB cable and put a 5 watt 50 ohm resistor I had laying around across the power wires, which draws about 100ma from the battery pack as long as the cable is plugged in. The battery pack no longer shuts down while powering the turntable. Of course, this wastes energy. A larger resistor (that is, a resistor with more resistance) will likely work, but I’ll leave finding the best value as an exercise for the reader.