Why do batteries run down?
Batteries contain some amount of an electrolyte and electrodes dipped into it which results in spontaneous redox reactions.
The Gibb's energy of such reactions are converted into electrical work and is used from suitable purposes.
But, as the reaction proceeds, the electrolyte gets used up and soon, the reaction stops and as soon as that happens, the battery's power generating mechanisms stop altogether.
Primary cells such as the dry cell or the mercury cell cannot be used again.
But, secondary cells like lead accumulator or the nickel-cadmium battery can be recharged and used again and again.
A good battery can undergo a large number of charging and discharging sessions.