They may exist, but I have never had or seen a digital VOM that didn't have a battery icon or one that flashed when the battery was low. Even the free and $2 ones from HF have battery icons.
My job in the Army and at Motorola was repair and calibration of electronic test equipment.
Swap the leads so you are using the same leads on each meter. They may look and feel ok, but could have corrosion where the wires connect or bad connectors themselves. Check the lead resistance on the lowest scale. Should be close to .2 ohms.