it is possible that the network connection has an issue. Check if the network card is selected to be powered down. You mention that it is intermittent and usually happens after one hour. If the network card is powered down, there might be an interrupt and thus your outlook exchange connection becomes offline.
Are you using pst local files on those machines or do you have the exchange 2003 (?!!) as your default mailbox? You mention that IMAPI is not running!! Are you using POP3 configuration or exchange configuration? If you are using POP3 configuration, you will be able to retrieve the mail from the exchange server but will not be able to share!! Make sure that if you have pop3 connection, remove it and reinstall exchange server connection instead!!!