Why does our immune system antibodies from covid-19 wear off after a couple months? does our immune system still recognize the virus?

This is not clear at present, The level of antibodies created by infection likely varies with individuals based on a number of factors. How long they persist at a protective level is also a matter of speculation until we have had enough time pass to get enough reliable data. If this behaves like other viral illnesses long term immunity may be present in some but not others.

Rapid decline of COVID-19 specific antibody in COVID-19 infected individuals allows short duration of immunity even if their immune system recognizes the virus. As a result, previously infected individuals still needs COVID-19 vaccination rendering longer immunity.

Although the antibodies wear off but the B and T cell memory is still there. If you get reinfected, those cells can produce antibodies quickly than the first infection. There are still a lot of unknowns regarding the Covid-19 virus, especially for reinfection cases.