They are right when claiming that they cannot always find antibodies after an infection and that antibodies can vanish fast. They are wrong when claiming that this means that the immunity got lost.  They cannot find antibodies when the adaptive arm of the immune system has chosen the killer T-cell path instead of the antibody path. It is possible to test for this type of immunity too, but it is very expensive. Basically you need to extract T-cells and mix them with real SARS-CoV-2 to see if the T-cells start fighting the virus.