Originally Posted by
PaperPrincess
A fusible featherweight interfacing adds body to the silk and will allow it to behave more like quilting cotton. It will also eliminate fraying so piecing will go better. Don't know what weight of SaS you used, but my guess is it was too heavy for silk. Also the adhesive is just temporary until you iron it so it may delaminate from the silk. Normally garment construction knowledge isn't necessary for quilting, but this might be one area that it helps.
I agree with PaperPrincess. A lightweight fusible would have been my choice. SaS is really just to hold things in place. It's made to hold the pieces there until you can stitch them down.