Question

Why dry cell becomes dead after long time

Answer 1

A dry cell has an electrolyte and a pair of electrodes. Even if the cell is not connected in a circuit, electrons /ions travel inside the electrolyte. Sometimes the rusted batteries cause leakages of current.  Due to the activity of electrons through the internal parts of the batteries,  the charges collected /stored in a new cell slowly get discharged. The cathodes get stacked with electrons..

so battery loses potential difference between two ends , gradually.

Answer 2

As electrolyte got finished and reaction gets completed