First of all, what router do you have? I had an old Linksys that would die like that - the connection would be solid but there was no traffic either way. Make sure you have the latest firmware.
I'm assuming your actual internet connectivity isn't the issue here, since it comes back when you restart the router but, to be sure, try attaching another device to your wireless network and pinging it (firewalls disabled) to see if data is getting across. If you can ping another device, the internet connection is at fault and not the router.
The easiest thing you can try is changing the channel, especially if it's still on the default value. Another device might be sharing the same channel and causing interference. If you do that, go up or down a few steps, not just one each time.
If you do have a Linksys router, try disabling UPNP. I remember that was the cause of my lockups back in the day.
Best, Paul