Since you are on a cable modem and you haven't said you're connected to a router between you and the cable modem, I'm going to assume you don't have one.
Try getting the IP address of the router built into your cable modem. It's usually set up to be your default gateway. You can find that setting by typing "ipconfig /all" from a windows command prompt. If you're running linux, try "ifconfig".
When you get disconnected on Monday afternoon, see if you can still ping the default gateway (cable modem). If you can ping the cable modem but you can't ping other sites on the internet (i.e.
www.yahoo.com), then your cable modem is having problems connecting to your cable provider.
If you can't ping your cable modem (defualt gateway), your cable modem may be resetting itself, your network card may be having problems, or the cable between your computer and your cable modem may have got unseated (unlikely if it happens every Monday afternoon....)
If you have access to another computer, or have a friend with internet access, have them try to ping your default gateway when your connection goes down. If they can ping it, it's probably something with your computer.
I forgot to mention, you might want to just give the tech support line for your cable provider a call, they may say something dumb like, "oh, yeah, Monday afternoon is our scheduled downtime."
Good Luck!