I have not yet run strace (as per Wietse's recommendation), but I think I may
have discovered the problem. My problem sounds very similar to the one
documented at the link below.
https://bugs.launchpad.net/ubuntu/+source/postfix/+bug/764096
I ran a quick test and, sure enough, the postfix-chroot.sh script that comes
with the Postfix package that I am using, seems to assume that all of the
required libraries are the 32-bit versions. A quick check with ldd shows that
this is, in fact, not the case. As this is the only 64-bit Postfix
installation that I administer, it makes sense that this would be the only one
with problems. I will test this theory soon by manually copying over the
64-bit libraries in the /var/spool/postfix and then test again. If it does, I
will make contact with the author of the script.
Thanks,
Jim