Exactly! If the antibodies from real exposure disappear from it in 3 months, how is vaccinated synthetic exposure going to any better job?? 
Antibodies are not the only things that work in your immune system to confer said immunity. In fact, they don't show up until there is already an infection, as they are energy intensive to produce and degrade over time. It is a very complicated dance. Antibodies never stick around long in your body... they get flushed out quite quickly following an infection.
Helper T cells are much more important. Helper T cells basically are the sentinels that activate the stored immune response (from prior exposure, natural or immunized) and send out the signal to start producing antibodies (if that type is stored in your immune memory). Basically, T Helper cells move around your body, programmed to look for a specific infection by querying cells it runs into. (Think "Driver's License, Please.")
Once it finds a strange response ("Officer, I left it in my other jacket...), it actually has kind of an IFF built-in, where it makes sure that what it sees isn't one of our own cells (This is why many types of cancers persist; they return the proper IFF code when queried). These are what maintain your immune system memory, not antibodies. Helper T cells communicate to another set of cells what antibody to make as well as antigens for whatever specific infection it has found, and also activate the killer T cell system.
In short, they're the watchdogs that have all the memory of your past infections, and control most of your response.
