Suggestions about how to solve this are welcome, the /var/log/maillog contents follow...
Working machine (swift)---------------
Dec 19 18:39:13 swift sendmail[3165]: alias database /etc/aliases rebuilt by root
Dec 19 18:39:13 swift sendmail[3165]: /etc/aliases: 64 aliases, longest 23 bytes, 652 bytes total
Dec 19 18:39:13 swift sendmail[3172]: starting daemon (8.12.10): SMTP+queueing@01:00:00
Dec 19 18:39:13 swift sm-msp-queue[3181]: starting daemon (8.12.10): queueing@01:00:00
Dec 19 18:39:13 swift sendmail[3183]: hBJNdDe3003183: from=<root@xxxxxxxxxxxxxxxxxx>, size=428, class=0, nrcpts=1, msgid=<200312192337.hBJNbPxu009075@xxxxxxxxxxxxxxxxxx>, proto=ESMTP, daemon=MTA, relay=swift.hockings.net [127.0.0.1]
Dec 19 18:39:13 swift sm-msp-queue[3182]: hBJNbPxu009075: to=root, ctladdr=root (0/0), delay=00:01:48, xdelay=00:00:00, mailer=relay, pri=120132, relay=[127.0.0.1] [127.0.0.1], dsn=2.0.0, stat=Sent (hBJNdDe3003183 Message accepted for delivery)
Dec 19 18:39:14 swift sendmail[3193]: hBJNdDe3003183: to=swift.root@xxxxxxxxxxxx, ctladdr=<root@xxxxxxxxxxxxxxxxxx> (0/0), delay=00:00:01, xdelay=00:00:00, mailer=relay, pri=30655, relay=mail.powergate.ca [216.183.11.6], dsn=2.0.0, stat=Sent (Ok: queued as 40D5F8753A)
Dec 19 18:39:20 swift spamd[3195]: server started on port 783/tcp (running version 2.60)
Dec 20 00:02:57 swift sendmail[4274]: hBK52vNY004274: from=mike@xxxxxxxxxxxx, size=274, class=0, nrcpts=1, msgid=<1071896576.4264.0.camel@xxxxxxxxxxxxxxxxxx>, relay=root@localhost
Dec 20 00:02:57 swift sendmail[4276]: hBK52ve3004276: from=<mike@xxxxxxxxxxxx>, size=434, class=0, nrcpts=1, msgid=<1071896576.4264.0.camel@xxxxxxxxxxxxxxxxxx>, proto=ESMTP, daemon=MTA, relay=swift.hockings.net [127.0.0.1]
Dec 20 00:02:57 swift sendmail[4274]: hBK52vNY004274: to=root, ctladdr=mike@xxxxxxxxxxxx (0/0), delay=00:00:00, xdelay=00:00:00, mailer=relay, pri=30274, relay=[127.0.0.1] [127.0.0.1], dsn=2.0.0, stat=Sent (hBK52ve3004276 Message accepted for delivery)
Dec 20 00:02:58 swift sendmail[4277]: hBK52ve3004276: to=swift.root@xxxxxxxxxxxx, delay=00:00:01, xdelay=00:00:01, mailer=relay, pri=30641, relay=mail.powergate.ca [216.183.11.6], dsn=2.0.0, stat=Sent (Ok: queued as DDFE087483)
Dec 20 00:06:03 swift sendmail[4361]: hBK563MH004361: from=mike@xxxxxxxxxxxx, size=276, class=0, nrcpts=1, msgid=<1071896763.4355.0.camel@xxxxxxxxxxxxxxxxxx>, relay=root@localhost
Dec 20 00:06:03 swift sendmail[4363]: hBK563e3004363: from=<mike@xxxxxxxxxxxx>, size=436, class=0, nrcpts=1, msgid=<1071896763.4355.0.camel@xxxxxxxxxxxxxxxxxx>, proto=ESMTP, daemon=MTA, relay=swift.hockings.net [127.0.0.1]
Dec 20 00:06:03 swift sendmail[4361]: hBK563MH004361: to=root, ctladdr=mike@xxxxxxxxxxxx (0/0), delay=00:00:00, xdelay=00:00:00, mailer=relay, pri=30276, relay=[127.0.0.1] [127.0.0.1], dsn=2.0.0, stat=Sent (hBK563e3004363 Message accepted for delivery)
Dec 20 00:06:04 swift sendmail[4364]: hBK563e3004363: to=swift.root@xxxxxxxxxxxx, delay=00:00:01, xdelay=00:00:01, mailer=relay, pri=30643, relay=mail.powergate.ca [216.183.11.6], dsn=2.0.0, stat=Sent (Ok: queued as 0C42287577)
Failing machine (james) ---------------------- Dec 19 16:53:47 james sendmail[2275]: alias database /etc/aliases rebuilt by root
Dec 19 16:53:47 james sendmail[2275]: /etc/aliases: 63 aliases, longest 10 bytes, 625 bytes total
Dec 19 16:53:48 james sendmail[2282]: starting daemon (8.12.10): SMTP+queueing@01:00:00
Dec 19 16:53:48 james sm-msp-queue[2291]: starting daemon (8.12.10): queueing@01:00:00
Dec 20 00:29:52 james sendmail[2740]: hBK5Tpwi002740: from=root@xxxxxxxxxxxxxxxxxx, size=350, class=0, nrcpts=1, msgid=<200312200529.hBK5Tpwi002740@xxxxxxxxxxxxxxxxxx>, relay=root@localhost
Dec 20 00:29:52 james sendmail[2742]: hBK5Tqhd002742: from=<root@xxxxxxxxxxxxxxxxxx>, size=601, class=0, nrcpts=1, msgid=<200312200529.hBK5Tpwi002740@xxxxxxxxxxxxxxxxxx>, proto=ESMTP, daemon=MTA, relay=james.hockings.net [127.0.0.1]
Dec 20 00:29:52 james sendmail[2740]: hBK5Tpwi002740: to=root, ctladdr=root@xxxxxxxxxxxxxxxxxx (0/0), delay=00:00:01, xdelay=00:00:00, mailer=relay, pri=30350, relay=[127.0.0.1] [127.0.0.1], dsn=2.0.0, stat=Sent (hBK5Tqhd002742 Message accepted for delivery)
Dec 20 00:29:53 james sendmail[2743]: hBK5Tqhd002742: to=james.root@xxxxxxxxxxxx, ctladdr=<root@xxxxxxxxxxxxxxxxxx> (0/0), delay=00:00:01, xdelay=00:00:00, mailer=relay, pri=30823, relay=mail.powergate.ca [216.183.11.6], dsn=2.0.0, stat=Sent (Ok: queued as 2F41F87579)
Dec 20 04:02:15 james sendmail[3114]: hBK92FcI003114: from=root, size=12001, class=0, nrcpts=1, msgid=<200312200902.hBK92FcI003114@xxxxxxxxxxxxxxxxxx>, relay=root@localhost
Dec 20 04:02:15 james sendmail[3117]: hBK92Fhd003117: from=<root@xxxxxxxxxxxxxxxxxx>, size=12297, class=0, nrcpts=1, msgid=<200312200902.hBK92FcI003114@xxxxxxxxxxxxxxxxxx>, proto=ESMTP, daemon=MTA, relay=james.hockings.net [127.0.0.1]
Dec 20 04:02:15 james sendmail[3114]: hBK92FcI003114: to=root, ctladdr=root (0/0), delay=00:00:00, xdelay=00:00:00, mailer=relay, pri=42001, relay=[127.0.0.1] [127.0.0.1], dsn=2.0.0, stat=Sent (hBK92Fhd003117 Message accepted for delivery)
Dec 20 04:02:16 james sendmail[3118]: hBK92Fhd003117: to=james.root@xxxxxxxxxxxx, ctladdr=<root@xxxxxxxxxxxxxxxxxx> (0/0), delay=00:00:01, xdelay=00:00:01, mailer=relay, pri=42524, relay=mail.powergate.ca [216.183.11.6], dsn=2.0.0, stat=Sent (Ok: queued as DF25D8783F)