First, install the Python bindings for gnome-keyring:

yum install gnome-python2-gnomekeyring
Download the file ~/.offlineimap.py and add the following settings in ~/.offlineimaprc. This assumes that you use a local IMAP server.

[general]

pythonfile = ~/.offlineimap.py

[Repository localhost]

type = IMAP
remotehost = localhost
remoteusereval = get_username("localhost")
remotepasseval = get_password("localhost")

[Repository Zimbra]

type = IMAP
remotehost = mail.example.com
remoteusereval = get_username("mail.example.com")
remotepasseval = get_password("mail.example.com")
Download the script imap-passwords and run it to add the IMAP usernames and passwords to your keyring. It will prompt you for server, username and password - use the same host names as in .offlineimaprc.

Now you can run offlineimap in a loop to automatically restart it in the case of some unrecoverable error, like so:

#!/bin/bash

while true; do
  /usr/bin/offlineimap
  echo Restarting in 60 seconds ...
  sleep 60
done
During the first run, gnome-keyring will ask you to authorize offlineimap to access your IMAP authentication data in the default keyring.

Thanks to Sebastian Rittau for the Keyring Python module.