Why does the battery display turn off while I'm using it? Is it factory defective?

No, it’s not.
The battery is designed so that the display automatically turns off about 10–15 seconds after activation to save power.

If the display goes dark, simply press the battery button once, and it will light up again:

OUT + number% means the battery is discharging, and the number shows the remaining battery level.

IN + number% means the battery is charging, and the number indicates the battery percentage.

This is a normal feature and not a malfunction.