well, some antibodies have physiologic role. I think all antibodies do not require to detect antigen from infectious agent. there is an interrupt in physiological trend of body. after the resolution of infection, the state is back to normal. so some antibodies with physiologic role are more or less produced.
All anti bodies are immunoglobulins which are proteins. they have a life of about 28 days. in circulation. As these proteins get recycled the levels may go down and disappear until stimulated by a booster dose.which will trigger further antibody production.
Regarding detection, they are highly specific to various components of the immunogen. So being specific to antigen, they will definitely recognise the antigens. Regarding detection, if you mean in-vitro detection, it may not mean that they fail to detect the antigen / immunogen. Probably, you could not demonstrate it. (they may be neutralising, agglutinating etc )