I never took on any purse rehabs with a similar issue, but I did fix a belt that was coming apart. I got a matching thread color and sewed together using the same needle holes. I had to use a beading needle because the holes were small. To tie off and anchor the old thread, I had to unthread a couples of stitches and glued the end down between the layers. To start the repair, I glued the end of the new thread in the same spot as the old and came up in the same hole where old thread ended. Oh, I also doubled the thread. Hope this helps!!!
Thank you for the responses soozlz & whateve. I'll give home restitching a shot!