If I close and restart Outlook on the client I regain the connection.

Solutions:
This article is related to all Window NT based systems:

Windows NT and Windows 2000 use two different "Autodisconnect" parameters; one for disconnecting Remote Access Service (RAS) connections and another for disconnecting LAN connections.

The RAS Autodisconnect parameter is documented in the Microsoft Knowledge Base article Q153944, but the LAN version is undocumented.

The only published reference to this Autodisconnect is in the Windows NT Resource Kit NT Registry Entries help file, in an overview of entries for the LanmanServer Parameters section.

"How Autodisconnect Works in Windows NT and Windows 2000"
http://support.microsoft.com/kb/138365/en-us

=====================================
Windows Autodisconnect

Found on: http://www.smallvoid.com/tweak/winnt/sharing.html

Decrease the timeout period for user connections, to close unused connections faster (Default 15 minutes):

"net config server /autodisconnect:1"

Inbound connections limit in Windows XP (NT-Systems). This limitation is NOT based on the number of LAN connections. Also often after 15 minutes the LAN connections are disconnected automatically.

More Info MS KB Q314882

=====================================
Network card's Power Management

Please check also the network card's "Power Management" options and the Windows power saving options. By default Windows is allowed to deactivate the network card to save energy. Check this in the network card configuration.

=====================================

Check the loosing network connection with the "Public Ping for Outlook".

Public Ping for Outlook: 

This freeware tool send every x-seconds a small package between the client and the server: "ping_EN.zip"

This constant "package" will normally avoid the failing of the network connection.

It is only a "test tool" to find out the reason why the network connection get failed.

If you run constantly this tool and the network connection do not get failed anymore, you must check your networkconnections, network cards, router, switch or power saving modes.