What does your Airport signal strength icon in the right-hand part of your Menu Bar show when this happens?
What are the lights on the Airport after this happens?
As far as re-establishing the connection, a somewhat faster method may be to open the Network pref panel, verify that "AirPort" is selected, and then click the "Advanced" button. you should now see a 'sheet' showing several tabs, with the AirPort one highlighted. Click the "TCP/IP" tab just to the right. If you have your connection set to "Using DHCP", there should be a button labeled "Renew DHCP Lease." Clicking that button should re-establish your connection.
However, the reason for losing the connection is still not answered. Do you have any apps that are using your connection while hidden? It may be that some app is trying to connect to a specific URL that is never completely loading its info.
The Strength is fully on, and the light on the airport is continuous.