My parents did that for years with The Boston Globe. Every August, they'd quit, and every September, they'd pick up a new 1-year introductory subscription at about 1/3 of the price.

I've been trying to get them to do the same with phone/Internet service - my Comcast is about half as much as their Verizon because I'm on a promotional 1 year subscription. Hell, just quitting FIOS, using dialup for a month, and then buying the exact same subscription they already have would save them $10-15/month.

Similar perverse incentives are at work in the job market (you usually get much better offers by changing jobs) and the housing market (apartments tend to jack up the rents as much as possible on existing tenants while offering move-in specials to new tenants). And people wonder why there's no loyalty in America anymore...