Okay, first of all, "range extender" is a misused term, but I can understand how you'd think it correct since all the companies call it that (scowl towards Netgear and Belkin). You either have a wireless repeater, which takes in wireless signal, and puts out wireless signal (sort of unreliable) or a wireless access point, which takes in wired signal and puts out wireless. If you have a wireless repeater, that's likely your problem. If you've got an access point, that could also be your issue.
Next time the WiFi goes out, open command prompt and try to ping 8.8.8.8, and run ipconfig. We need to know if you are falling off your LAN completely, or if you're just suddenly unable to access the internet.