Try to open "Console" and see if it prints any messages from Wallpapery such as "Failed to contact server" or similar.
Also, does it refresh the wallpaper if you close Wallpapery (click menubar item and select "Quit Wallpapery") and then reopens it?
Have you changed some internet settings which might cause this such as setting up a proxy server, tethering on your phone (using iPhone "hotspot" functionality) or similar?