What happens after that depends on a number of factors, including the level of organics in the water, 02 levels, etc, and eventually it breaks down and is no longer effective.
Prime contains hydrosulphide salts, which is a reducing agent. That's why it reacts with chlorine compounds, which are oxidising agents. This is also why it will neutralize bleach after one sanitizes their tank. If there are no chlorine compounds left in the aquarium water it will find something else to reduce such as 02 (oxygen).
Personally my only real concern is what my disinfectant is (chlorine or chloramine), at what level ppm or mg/l (same thing) so I can determine what level of conditioner (Seachem Safe) I need to render my tap water safe for my fish.