The file /etc/postfix/master.cf of postfix-2.1.5-4.2.RHEL4.x86_64 contains a hard-coded path to Cyrus-IMAP LMTP deliver agent, /usr/lib/cyrus-imapd/deliver. However, this causes problems on x86_64 systems since Cyrus-IMAP LMTP deliver agent path is /usr/lib64/cyrus-imapd/deliver.
Fixing this problem is easy: just edit /etc/postfix/master.cf and replace /usr/lib/cyrus-imapd/deliver with /usr/lib64/cyrus-imapd/deliver.
I have filled in a bug report against Red Hat’s Enterprise Linux 4:
https://bugzilla.redhat.com/bugzilla/show_bug.cgi?id=192601