We have two XPS 13's with WD15 in service at the moment, with two more waiting in the wings.
One system seems to work fine, with the XPS 13 cover open and using the XPS 13 keyboard along with a Logitech Unity wireless mouse and an external monitor + Ethernet hard wired to the WD15. The other system was problematic, the difference being that it was trying to be used with its cover closed when connected to the WD15. We finally figured out that the XPS 13 needs to be first connected to the WD15 while open, then turn off the Wi-Fi before closing the cover. This seems to have "fixed" the problem. The problem being that the Ethernet adapter would disconnect, shut down, whatever and then come back on briefly. After a few minutes (or less) of this the external monitor would go off. Opening the XPS's cover would usually bring things back to life.
Simply turning off the Wi-Fi before closing the cover seems to be the key for us! We have the settings set in the Power Setting so that Nothing should happen when the cover is closed.
We have Installed the latest updates (as of 11/22/2016) including BIOS 1.4.10. Lowered the Wi-Fi power output down to 75% as suggested elsewhere, etc. This didn't correct the problem, only turning off the Wi-Fi before closing the cover has helped.
Even with the Realtek Ethernet Adapter disabled, and the Ethernet cable disconnected from the WD15, when we shut the cover of the XPS 13 with the Wi-Fi on - the WD15 becomes unstable. We have an external USB drive attached to the WD15, the USB connection comes and goes, losing the drive. The Realtek Ethernet adapter disappears from the Network Adapter list, etc. Opening the XPS 13 cover helps but not everything recovers. It usually takes a reboot.
Again, we seem to be OK when the XPS 13's cover is open. And OK - if we turn off the Wi-Fi - before closing the cover.