ips logs return messages such as:
net.bluemind.ips.vertx.ProxySession WARN - Closing connection from /192.168.0.0:33333 as it failed to authenticate for 30sec.
When the maximum number of IMAP processes has been reached, users get login errors.
bm-ips may also no longer accept any connections.
You need to increase the maximum number of IMAP processes.
In general, you need to allow for 1.5 the number of users for a mixed webmail/thick client use. On installations where many users use thick clients, you need to allow for approximately 3 times the number of users.
Count the number of processes used currently:
pgrep -c imap