The changes Matt suggested need to be done from the VPN admin console to enable/disable split tunneling
On the client, after the VPN is up, what do you see for the gateway when you do an ipconfig/all from a command prompt? If you see 0.0.0.0 or a blank entry, chances are high that split tunneling is enabled and that Outlook now uses the Network Connectivity Sensor for checking accessibility. Unfortunately, it is incompatible with split tunneling.
Are you able to login to the admin console and change to split tunneling disabled and test to see if there is a positive change in behavior?