Other batteries work fine with that atomizer?
You charged it for 12 hours, and it still acts as though the battery is dead after you puff eh?
Most self regulating batteries for electronics use a simple op-amp set up as a voltage comparator with the reference voltage determined by a resistor and zener diode to verify battery levels.
It's quite common for the reference line on an op-amp to have the wrong resistance, or to stop bleeding off through the zener diode prematurely (wrong breakdown voltage).
During use, the voltage available for the comparator circuit is decreased, but the reference line should be set at a level such that it takes into account this voltage drop.
These things should ideally be checked by the manufacturer during the build... but as with most production lines, they probably use a 10% check rate, or a moving check rate that's overstayed it's welcome.
Unfortunately, it wouldn't be easy for the Vendor to verify the low power indicator is good without smoking it themselves start to finish. So I wouldn't place blame on the vendor.
These things aren't user serviceable to my understanding.
You can do the obvious, and check for metal flecks or oils on the battery contacts... that could cause a short path which would trick the level indicator, but that's not likely.
Beyond the obvious visual checks on the outside, there's nothing you can really do about it.
In short, yeah, replace the battery. But don't be harsh on the vendor.
