Does the salt bridge in a galvanic cell deplete over time?
Consider a salt bridge as a part of the cell electrolyte, that is not allowed to mix with the rest of electrolyte.

For a particular ion, there are 2 cases:


The ion is shared with the electrolyte part, from which the ion migrates toward the bridge. Then the ion gets depleted from electrolyte and not from the bridge.
The ion is not shared with the electrolyte part, from which the ion migrates within the bridge toward the other electrolyte part. Then the ion gets depleted from the bridge.


But there is needed to add the bridge maintains ion neutrality, so ions that leave the bridge are replaced at the other bridge end by the same or other ions of the same total charge.

Bridges are not usually used in power cells and cells where significant portion of chemicals gets depleted or react. If they are used, they usually use at least one of ions shared.

Power cells often use a single electrolyte and a diaphragm, soaked with this electrolytes, so ion depletion does not apply.

Bridges are used mostly in cells where accurate potentials matter, to minimize phase potentials, where the current is minimal. Like calomel ( $\ce{Hg2Cl2}$ ) or $\ce{AgCl}$ reference cells, or in laboratory test cells.