When the battery runs low, the meters can fail to give an accurate voltage reading, resulting in the operator falsely believing the electrical power is off or low. This poses an electrocution hazard.
Actually, if you use the Prove-Test-Prove method on your test equipment, on a known
source of voltage, before and after you've tested something, this sort of thing shouldn't happen.
Having absolute faith in the integrity of your test gear (especially the battery operated stuff) is what is known as complacency.
Complacency kills electricians.
Let's face it, these days if you're not young, you're old - Red Green