Remember that a seam ripper is not designed to plow through stitching. Sometimes you will confront stubborn stitches. Take a deep breath and remain patient. Plowing through those stubborn stitches is apt to cut your fabric and render the fabric unusable.
Start removing the stitches as previously described. At an area where the stitches are removed, open the seam so that the stitches are exposed in the seam line.
Use the tip of the seam ripper to cut the stitches in the seam line. Pull the seam ripper away from the fabric rather that toward the remaining stitches. It takes more time than plowing the seam ripper through the the stitching but it is much less likely to cut the fabric.
If a cut in the fabric does happen and it is not in an area that is visible, immediately use fusible light weight interfacing on the wrong side of the fabric with the cut closed as closely as possible. Waiting to do this step can cause the edges of the cut to fray and the cut will always be visible. The cut will weaken the fabric no matter what but in most cases the fusible interfacing can mend the cut if it is inside the item you are sewing.