When your body is exposed to disease it produces antibodies. This usually provides protection from same disease in future so it is like training soldiers to fight a certain battle.
By design, antibodies stick around "ready for action" should they be needed. They are not the disease, they are just a marker of disease and the thing designed to fight it now, or in the future.
With Hep C, the antibodies only work in 25% of people, so they are like "broken soldiers" but they still hang around indefinitely.....
Over time (if the disease is not seen again, and thus the soldiers remain un-needed) antibody levels fall. It's like they get put out to pasture, like old doctors, soldiers or horses.
For example after Hep B vaccination some people become undetected for the protective surface antibody after 5-10 years. Similarly some (but not all) people who are cured of Hep C will eventually have undetectable antibodies.
About 50% of people will lose detectable antibodies by 10 years post SVR.