Internet connection fails very frequently!

Based on this information, I believe you should be setup with a Dynamic IP Address, which is what the majority of the Cable Companies use. Which means that when you log onto you ISP you are handed an address which might be something like 70.108.23.39, which is your WAN address. That IP address remains with you until your ISP changes it or you perform a release and renew, at which time you are handed a new address.
You will note there should be a function in your router setup for your router to act as a DHCP Server for your LAN and here you can indicate what range of IP addresses will be handed out to your LAN notes (meaning the 4 workstations connected to your router ports). If your router address is 192.168.0.1, then your LAN IP address will be of this configuration, always as 192.168.0.???. So, you can set your DHCP LAN range from 192.168.0.100 to 192.168.0.254 or whatever range you might choose. Which means when your workstations logon they would recieve addresses within this range. The range of addresses below this 192.168.0.2 thru 192.168.0.99 could be used for static IP address within your LAN, which would require a slightly different setting for the TCP/IP and we will discuss that later. However, you should go into the network adapter control panel on each of the workstations and in the TCP/IP settings configure both IP and DNS addresses for dynamic, then click the advanced button and set the Gateway address to 192.168.0.1, which is the address of the router. This will direct the workstations to the router which will be acting as a gateway to the network. So, the WAN address is your Wide Area Network address which how the internet finds your modem and your modem should be pointing to your router (192.168.0.1), which defines your LAN. The last number in the LAN address indicates the node and so the router communicates with the workstations through this gateway.
Once your have accomplished this and successfully connected to the internet. You should look at the status screen in your router and make note of your WAN address, and the DNS addresses provided by your ISP connection.
Then if you wanted to setup your LAN as static IP addresses, meaning your workstations woulld always have the same addresses, you would do the following. In the Network Adapter Control Panel. Go to TCP/IP applet and set for Static IP at each workstation. Making the first one 192.168.0.10, the second station 192.168.0.11 and so on. And on all of them set the mask to 255.255.255.0, the gateway to 192.168.0.1, the two DNS setting to whatever the DNS was indicated in the Status Screen of your router and you now would have static IPs for your LAN workstations. Static LAN IPs have distinct advantages over dynamic for security purposes, which a whole different lesson.
Well, I hope this is clear, I tried my best to make it clear...Good Luck and let me know how your make out.
Just as side bar, I have numerous client's with cable ISPs and they also have connectivity problems from time to time. And oddly enough they eventually seemed to clearup even though the cable techs claim that the problems are not caused by their equipment????