It is fused on. The fabric quality is very good and the weave is normal - not loose or cheap... The biggest place it's happening are on the large wheels (spokes) of an antique baby carriage. Since it's circular, bias or not wouldn't make a difference. I didn't even consider anti fray of any kind, since I've never needed it before. I'm going to try another needle....

Are you using a very short stitch length. A .5 is the best for me. I also make sure that the edge of my satin stitch is on the edge of the applique, and the rest of the stitching is on the applique.
I also love Fray Check.
Hope this helps.

Maybe I'm not hitting the outer edge well enough.

I put my needle right on the edge of the applique piece, not on the applique itself. As I sew, the needle rides along the edge.

I agree with the others, looser woven fabric will fray a bit more, even with a fusible on the back.

I just got through with an appliqued block and I noticed on the pieces where I didn't hit the outer edge right, it frayed.

You might try double-stitching. With this method you do a narrower satin stitch not too close together first, then go around again and do your regular satin stitch on top, a little wider and closer together than the first.