In all liklihood one of two things is happening. Simple one first:
Outlook sets itself up in "Caching" mode to connect faster in the office (by default.) In settings there is a check box you clear to turn this off. 80% chance that will fix it.
Per Microsoft:
On the Tools menu, click E-Mail Accounts, click View or change existing e-mail accounts, and then click Next.
In the account list, click the Exchange Server e-mail account, and then click Change.
Under Microsoft Exchange Server, clear the Use Cached Exchange Mode check box.
Exit and restart Outlook.
More of an issue:
Your VPN may be functioning through a firewall that is blocking RPC/Port 135 -- which Outlook uses to make the connection.
Open the port and it should be fine.
Please note that a lot of companies have temporarily shut off 135 in the last few days due to a virus outbreak that was exploiting the open port -- so that may be contributing to your issue.
Good luck!