Hi Cindy,
Now I wouldn't call myself anykind of expert when it come to applique but I do love it and I don't think I have had the same problem with the backing fabric, so this might me helpful. - I usually use a bondaweb (or some other lightweight fusible fabric) I like it because I can draw on the paperside, cut it out easily, remove the paper and attach it to my backing firmly once ironed (also this means I can work without any, or just a few pins, and this is always a good thing as I always seem to find the sharp ends!)
The only solution I can come up with is to check your machine tension, stitch length or replace the needle? (this is usually what I try when in doubt!)
Hope the experts on here manage to figure it out for you.
Happy sewing!
Yvie