Antibodies (Immunoglobulins) will fade over time, and may not be detectable in the blood after a while. So a negative antibody test for Covid-19 wouldn't necessarily mean you're not immune.

However, immunity should persist for a long time, perhaps even for life. That's because the immune system retains memory of past pathogens and knows how to make new antibodies quickly if needed.

The reason we seem to keep getting infected with cold and flu, year after year, is because these are actually different viruses each time.

You are carefully explaining the mostly true generality.

The fact remains, we simply don't know how long immunity will persist for a given novel virus. We will find out over the next months and years, but at this time, we do not have concrete knowledge about SARS-CoV-2.