Just increased the maximum number of IMAP (courier) connections (for thunderbird and Mac users) in /etc/courier-imap/imapd
as discussed here.
MAXDAEMONS
from 40 to 80MAXPERIP
from 4 to 40as discussed here.
I also set DEBUG_LOGIN=1 from DEBUG_LOGIN=0
so I could use Munin to count the IMAP logins in the maillog.