While there are various attempts to administer COVID-19-convalescent plasmas to SARS-CoV-2-infected patients, neither appropriate approach nor clinical utility has been established. We examined the presence and temporal changes of the neutralizing activity of IgG fractions from 43 COVID-19-convalescent plasmas using cell-based assays with multiple endpoints. IgG fractions from 27 cases (62.8%) had significant neutralizing activity and moderately to potently inhibited SARS-CoV-2 infection in cell-based assays; however, no detectable neutralizing activity was found in 16 cases (37.2%). Approximately half of the patients (~ 41%), who had significant neutralizing activity, lost the neutralization activity within ~ 1 month. Despite the rapid decline of neutralizing activity in plasmas, good amounts of SARS-CoV-2-S1-binding antibodies were persistently seen. The longer exposure of COVID-19 patients to greater amounts of SARS-CoV-2 elicits potent immune response to SARS-CoV-2, producing greater neutralization activity and SARS-CoV-2-S1-binding antibody amounts. The dilution of highly-neutralizing plasmas with poorly-neutralizing plasmas relatively readily reduced neutralizing activity. The presence of good amounts of SARS-CoV-2-S1-binding antibodies does not serve as a surrogate ensuring the presence of good neutralizing activity. In selecting good COVID-19-convalescent plasmas, quantification of neutralizing activity in each plasma sample before collection and use is required.