External Monitor Problems Only When Lid Closed

I have a brand new XPS 15 that is experiencing an unusual issue.  I have two external monitors connected:  one via HDMI and one via a DisplayPort->DVI converter.  Both work absolutely fine while the laptop lid is opened (it makes no difference if the laptop display is disabled or enabled).  However, if I close the lid and click on the Network icon in the system tray, it will disconnect both external monitors for a brief time and then reconnect them.  This is reproducable in 100% of the cases, with the only difference being if the lid is opened or closed.

This wouldn't be that bad if that was the only instance, but I also occasionally experience these drops at random times.  I'm thinking that it might be correlated with a notification coming through or something in the system tray popping up, but I'm not sure.  As you can imagine, it's frustrating to lose your monitors for 3-5 seconds at a time.  I have downloaded and applied all up-to-date drivers for the system, and have changed various power settings with no effect.  Any help would be greatly appreciated.