Dovecot: Warning “client_limit (1000) reached, client connections are being dropped” appears in maillog

Issue

• The following messages appear in /var/log/maillog.

imap: Error: net_connect_unix(/var/run/dovecot/stats-writer) failed: Resource temporarily unavailable
master: Warning: service(stats): client_limit (1000) reached, client connections are being dropped

• Users sometimes fail to access their mailboxes.
• The parameters like client_limit and process_limit have been tuned for POP3 and IMAP4.
• On the other hand, there is no additional tuning for stats service. (It uses default configuration.)