If Whm/Cpanel/Webmail is not loading in ssl mode (2087/2083/2096) then first you can try
httpd (stop/start/restart)
If it not works then https authentication is usually run by the stunnel for c-panel; and since the error is shown only when data transfer using stunnel is done; you can try a stunnel restart.
do the following:
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ps ax | grep stunnel
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you will get a pid for the current running stunnel. Kill it via:
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kill -9 pid
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now start stunnel: /usr/local/cpanel/etc/init/startstunnel
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then restart exim and cpanel via the “/etc/rc.d/init.d/” start/stop directives.
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OR simply
start stunnel: /usr/local/cpanel/etc/init/startstunnel