Outlook uses the settings of Internet explorer. So you would assume something is up with internet explorer that is causing outlook not to connect.

I would check the connection settings table in IE, under tools, option, connection tab,
then under LAN, see if the auto detect settings is checked. Also if you are using a proxy check your proxy connection settings.

Also check the settings of the network device to make sure that it is set to always connect.

Also:

Try this.
Open OE and click on
TOOLS / OPTIONS / SEND
Check SEND MESSAGES IMMEDIATELY
Then click on APPLY / OK

Also, try to change the settings via the accounts and override the default connection settings for each account. Go to tools/accounts/all, and select the account that you want to change the settings for, then select properties, connection, and check the box there "always connect to this account using..."

And then select from the drop down menu your connection choice. You can also add a new choice as well.. and set it up that way.

Hopefully one of these tips can help you get this resolved.