It sounds as if your wi-fi is set to sleep after 15 minutes.
Try this to check: Menu (the capacitive button below the screen), settings, wireless & networks, wi-fi settings, menu (the capacitive button below the screen), advanced, wi-fi sleep policy. Make sure it is set to "never." Right after setting up my Spectrum, I was having issues with it remaining connected to my wi-fi at home. Changing this setting was the perfect solution.
If this does not help, I'm not sure what will. But right above the wi-fi sleep policy setting there is a setting called regulatory domain, which controls how many wi-fi channels the Spectrum looks for. Perhaps your setting is 11 and your router is using 13 or 14 channels?
Hope this helps.