Just to confuse you further Anne, you may be putting side pressure against the blade this will cause your blade to flex to the side and the friction against the side of the blade will make it heat, once it gets hot enough the tempering which toughens steel is lost, it's just a matter of time till it breaks. You can take a paper clip and bend it back and forth at one place after a bit it will break at that point, this may be what is happening to your blades. I would suggest you try some simple practice cuts and pay attention to where and how you are pushing the wood into the blade, you may find this is what is happening, make sure the blade is TIGHT loose blades break quicker!
Save your money and get a better saw, Ryobi is about bottom on the chart. ten years old probably no replacement parts available.
Good luck, and don't get discouraged,
Gabby