Battery reads 5V but can't power a 5V sensor?
Try putting a load resistor across the power pack output lines and see if it wakes up. Try ~20 Ohm for a short while, that would waste some 1.25 W so don't burn your fingers... If it wakes up, you could easily make a periodic load that keeps the pack alive:







simulate this circuit &ndash; Schematic created using CircuitLab

How often you need to pull the load needs some experimentation. There is of course a possible flaw with this circuit: it's not self starting. But that could be a topic for a new question.