I'm seeing the message inetd[334]: imap/tcp server failing (looping), service terminated on a RedHat_ 5.2 system, causing imap connections to be refused. The imapd in use is Washington Univers 12.250. Could this be anything to do with Exim?

No, it's nothing to do with Exim, but here's the answer anyway: there is a maximum connection rate for inetd. If connections come in faster than that, it thinks a caller is looping. The default setting on RedHat_ 5.2 is 40 calls in any one minute before inetd thinks there's a problem and suspends further calls for 10 mins. This default setting is very conservative. You should probably increase it by a factor of 10 or 20. For example:

imap stream tcp nowait.400 root /usr/sbin/tcpd /usr/local/etc/imapd

The rate setting is the number following nowait . This syntax seems to be specific to the Linux version of inetd. Other operating systems provide similar functionality, but in different ways.