I don't understand... Why is it slowing down? Have you called your ISP? You shouldn't be asking why your temporary fix didn't work, you should be asking why it needs to be reset in the first place.
Is the cable modem overheating? Or the router?
What more than likely is happening is that when you reset your modem you're not giving it enough time to obtain a DHCP address (assuming it's using DHCP) before you reset your router too.
Unplug power from both the modem and the router completely - after about 30 seconds plug the cable modem back in. Wait a minute or as long as it takes for your cable modem to establish an IP address, then plug the router back in.