I have had that prob and thought i would a)unpick a little bit and satin stitch using my normal everyday sewing machine or b) move tha material closer to the satin stitch and sneak in a little bit fabric glue i havent decided which one to do yet but i may just end up doing that whole block again im in the thinking process as i didnt want to ruin it good luck :)

Yes, you will have to do it again.
OK, I am just teasing. How big is it? You might be able to fix it by hand. Just try to slip stitch the little piece in place so it does not fray.
Give you a tip on applique. It should have 3 rows of stitching. The first is the placing stitches. That stitches out first and you put your fabric on that. BUT don't cut the fabric the exact size, leave it bigger. The second row if stitches are the fixing stitches. These stitch the applique fabric on your base fabric, then you take the hoop of the machine and trim the fabric back to the fixing stitches as close as you can.A pair of curved embroidery scissors are great for this. Do not take the fabric out of the hoop.Put the hoop back on the machine and it will do the applique stitches.And you have a perfect piece of applique.

good luck..and a great question for all of us that have not had the courage to get too far in to applique. Ii have many designs just need to work up the courage....

Thanks for asking, I learned something new too. I haven't done that much applique either. :) *4U

Happened to me once in a while. I cheat. I leave the thread and bobbin on and repair with a slightly wider satin stitch, everything still in the hoop but the embroidery unit removed of course.

Lisa, I believe you got the answer I would have given to you - or try to move your stitching line back and stitch it a second time - on my machine - I can go back or forward to the next color stop - try it - see what works for you.