to Cable Forum
It's unlikely that it is anything to do with the cable modem. That either provides an internet connection, or it doesn't.
I would therefore suspect something odd in your router or network configuration.
Presumably you are setup as modem <> ethernet <> router then wired and wireless to computers.
Are all the computers on the same workgroup? Do they obtain their IP address automatically (not fixed) from the router's DHCP? Do you have current network drivers on your computers both wired and wireless?
If it's just the wireless dropping out try changing the channel being used by the wireless on the router. Do you have any QoS enabled? Is one computer hogging all the bandwidth? Does the router have the current firmware? If you've done lots of fiddling with the router settings maybe a factory reset will get it back to basics. Are there any firewalls running on computers that could be rejecting connections?