How could a rechargeable battery charge itself without an external source?
The chemical processes that happen inside a battery when it is being discharged take time to occur - if they cannot keep up with the load on the battery the voltage will drop and it will be seen as dead. One name for this is polarization.

If the battery is left for some time the chemical processes can catch up and you can then discharge the battery again until it is discharged.

Usually the time for subsequent discharges will be shorter and shorter until the battery is really dead.

The speed of chemical processes happen faster at higher temperatures so warming up the battery can provide more output before the battery output collapses and recover more quickly.