If the flow of water across a fish's gills were to stop, why would gas exchange eventually cease even if the blood continued to flow?
The concentration of oxygen in the water surrounding the gills would become equal to that in the blood, eliminating the diffusion gradient.
The lack of water pressure would cause the gill filaments to expand and block the capillaries.
The fish would no longer be able to produce the ATP required for the active transport of gases.
Oxygen molecules can only diffuse through moving water and cannot move through still water.