The SARS-CoV-2 pandemic poses the greatest global public health challenge in a century. Neutralizing antibody is a correlate of protection and data on kinetics of virus neutralizing antibody responses are needed. We tested 293 sera from an observational cohort of 195 reverse transcription polymerase chain reaction (RT-PCR) confirmed SARS-CoV-2 infections collected from 0 to 209 days after onset of symptoms. Of 115 sera collected ≥61 days after onset of illness tested using plaque reduction neutralization (PRNT) assays, 99.1% remained seropositive for both 90% (PRNT₉₀) and 50% (PRNT₅₀) neutralization endpoints. We estimate that it takes at least 372, 416 and 133 days for PRNT₅₀ titres to drop to the detection limit of a titre of 1:10 for severe, mild and asymptomatic patients, respectively. At day 90 after onset of symptoms (or initial RT-PCR detection in asymptomatic infections), it took 69, 87 and 31 days for PRNT₅₀ antibody titres to decrease by half (T_1/2) in severe, mild and asymptomatic infections, respectively. Patients with severe disease had higher peak PRNT₉₀ and PRNT₅₀ antibody titres than patients with mild or asymptomatic infections. Age did not appear to compromise antibody responses, even after accounting for severity. We conclude that SARS-CoV-2 infection elicits robust neutralizing antibody titres in most individuals.