Hi I did some research on your new DELL XPS 13, however since I dont have the exact model number and I don't have acces to your device its a little hard to find the cause.
But... It turns out that it's common for a DELL XPS to have problems with your wifi connections this is because of the basic stock wireless card that the manufacturer put inside.
The stock wireless card is cheap and bad, to be more precise users are having a hard time finding or creating a stable connection between the wireless card and your (wireless) router.
(Check how many bars you get on your wifi signal)
You could try and update your driver for the network card and/or BIOS, asuming you still have the stock model it should we easy to find the right drivers, and this should help!
Alternatively you could move closer to the source of your wifi (That would be your Router or AP "Acces point") and see if that helps OR replace the wireless stock card for a new one.
(Costs will roughly be around 20$)
There is also be the possibility of a "Time Out" function inside your router that could have been enabled, this option is there to kickout any device that's inactive for a set amount of time.
However I don't think this is the cause of your issue.
Let me know if this information was helpfull
Edited by Cortiz, 05 February 2017 - 10:19 AM.