I have a D-Link 300T in the menu 'Setup', section 'Connection', I have two features. One called "Keep Alive:" that I have set to 99999 mins and the other, is a check box labeled "On Demand:" which I have un-ticked or blank if you like.
I don't think D-Link vary their software interfaces that much between models...
I was back at my friends house the other day and could find no setting limiting the amount of internet time, the only setting with a limit was the DHCP IP Lease time which was set to 24 hours, presumably it resets everytime a PC logs onto the LAN.
MMmmmmm I have to say I'm a bit stumped. I don't think the WiFi is an issue or the DHCP lease time.
On My D-Link, I do have something similar happen but it is a random occurrence - namely that despite it saying everything is connected on lights and interface, in reality it isn't. a good old re-boot usually fixes and I have tried a replacement model with the same s/ware both act the same.
Speaking of which, have you checked the firmware or software version is current on your router there?
dig about in the support section of the D-0Link web site and compare the version installed on the router to that which is current - you may need to flash it up to a more current version...