Welcome to this site, Nancy! But, you might have better luck with an answer to scrollsawing problems at the scrollsawing forum.
Scroll Saw Woodworking & Crafts Message Board
However there are a few folks around this site who use scrollsaws to cut out carving blanks, so you might get some blade information here, too.
I don't have a scrollsaw, but an old clunky Boise Crane jigsaw that sort of serves the same purpose. I've found that most blade breakes are caused by feeding the stock into the blade at an angle. You can rotate your work but make sure you always feed directly into the teeth and don't ry to force the work at all sideways. If you are cutting heaview material, you might try going to a bit coarser blade or a skip tooth blade. Still most of the blade break problems are caused by not feeding straight into the cutting teeth on the blade. Hope that explains things so you can understand.
Here's a good practice to get used to feeding directly into the blade. Just try some straight cuts.....that is exactly how you will feed material into the blade even when making curved cuts. Rotate your work around the cutting edge, but be careful to always feed directly into the teeth, and not push the blade at all to either side.
You will probably get some good advice on which blades are the best brand, but keep in mind that if you feed the work into the blade wrong, any blade will break.
Al