Yes, you have up to the time the mfg warranty expires to purchase the manufacter's extended warranty. The rate sheet may go up over time however.
I compared Mazda's warranty with the one from AAA and saved myself about $700 compared to the rates I was quoted. They have rates with $50, $100 and no deductible which affect the premium greatly. I have the NO deductible for 7 Years/100000 miles and it was about $1600. It was 1 more year than the Mazda and much cheaper. It's also backed by AAA so if you have problems, they stand behind you (sometimes requires a little nudging).
I purchased the extended warranty from the dealer using the company The Mechanic for 60 months and 60,000 miles, for $1,860. I am going to cancel that partly because I don't think they deserve any other business from me. Long story short, the sales manager was very rude when I took delivery of the car.