SARS-CoV-2 antibody-positivity protects against reinfection for at least seven months with 95% efficacy https://www.thelancet.com/journals/eclinm/article/PIIS2589-5...
But not everyone develops long-lasting antibodies and not everyone keeps those levels high.
In this study, 8-30% didn't develop/lost antibody positivity (depending on which test method used): https://wwwnc.cdc.gov/eid/article/27/3/20-4543_article
In this study, 28% of those with documented infection had their antibodies go below the level of positivity over time: https://www.cdc.gov/mmwr/volumes/69/wr/mm6947a2.htm
True. It depends on which specific antibody you look for, and how.
Here's a recent cohort study:
Anti-SARS-CoV-2 Antibodies Persist for up to 13 Months and Reduce Risk of Reinfection https://www.medrxiv.org/content/10.1101/2021.05.07.21256823v...
"Here, we longitudinally measured Spike (S) and Nucleocapsid (N)-specific antibodies in 1,309 healthcare workers (HCWs), including 916 COVID-19 negative HCWs and 393 convalescent COVID-19 for up to 422 days post-symptom. ... Overall, 69 SARS-CoV-2 infections developed in the COVID-19 negative group (incidence of 12.22 per 100 person-years) versus one in the COVID-19 positive group (incidence of 0.40 per 100 person-years), indicating a relative reduction in the incidence of SARS-CoV-2 reinfection of 96.7% (p<0.0001)."
Of course, these antibodies <--> protection studies are a bit of streetlamp effect phenomenon. Antibodies are relatively easy to measure so that's what immune endurance studies tend to check for. The relative risk of reinfection in real-world settings is the more robust measure.