Re: [exim] malfunctioning email delivery after upgrade to Ex…

> == rcpt@??? R=xxx (-36): host lookup for <imap_server> did not
> complete (DNS timeout?)
>
> There is no problem with DNS resolution of the relevant domains on those
> MX servers whatsover, judging by using dig and host command in shell.

A dig or host command once is not a proof.

#!/bin/sh
while true
do
/usr/bin/time -a -o /tmp/timelog dig +short <imap_server> mx >/dev/null
sleep 0.2
done

> On IMAP servers receiving emails from the above MX servers, the new and
> very frequent error is now this (even when the mid corresponds to just
> one recipient):
>
> <mid> no immediate delivery: more than 10 messages received in one
> connection

You need this setting:

> smtp_accept_max_per_connection = 100

for the receiving Exim (you call that "IMAP servers").
And restart Exim.