Why does the mercury cell have a constant cell potential throughout its useful life?

Hint: The cell potential of any cell is maintained by the movement of ions. If the ions are used up completely the cell potential will become zero and stop working.

Complete Step by Step Solution:
Silver \[\left( {Ag} \right)\]is a significantly less reactive metal due to which it does not easily undergo corrosion and does not easily oxidise
.
When Silver comes in contact with air it forms a silver oxide \[\left( {A{g_2}O} \right)\] which when comes in contact with hydrogen sulphide \[\left( {{H_2}S} \right)\], a black silver sulphide \[\left( {A{g_2}S} \right)\] layer is formed on the surface of the silver.
The chemical reaction for the oxidation of silver can be written as
\[2Ag + {O_2} \to A{g_2}O\]
\[A{g_2}O + {H_2}S \to A{g_2}S + {H_2}O\]
Thus, when a black silver sulphide \[\left( {A{g_2}S} \right)\] layer is formed on the surface of the silver we can recognize that silver gets corroded.

The corrosion of silver can be prevented by avoiding exposure to an open place that absorbs moisture and tarnishes silver.

Additional information: If corrosion occurs in iron it is called rusting of iron. When iron is exposed to air and moisture, it forms a layer of iron oxide which is rust. Rust chemically is hydrated iron (lll) oxide \[F{e_2}{O_3}.{H_2}O\].
Rusting of iron can be prevented by galvanization and paintings. Galvanization is the process of applying the coating of zinc which prevents the oxidation of iron.

Note: Generally, in a dry cell the cell constant is maintained due to the movement of ions that after a certain period of time completely use up and stop working.