It could be either cable modem or router - which brands do you have? Few years ago my cable modem went bad. Replaced with a generic brand from Best Buy but it would drop too often. Replaced with Motorola Surfboard and has been going fine! 
I also use a splitter - have been for years - and haven't had any problems. However, I've had both cable modem and router go bad and that usually results in dropping connections. How long have you had the router? As with any electronics, difficult to say how long they'd last. Sometimes they go for years, other times you get a lemon and it conks out quickly for no apparent reason. But if you've had your cable modem for 6 years, that might be the issue - that's about how long my first one lasted.
Last edited by NickC; January 31st, 2011 at 10:27 AM.
My equipment:
Acer Aspire AX3300-U1322 Desktop (sorry didn't build this time!), 4Gb RAM, AMD Athlon II quad core CPU