@PamNY, no the bungee came unhooked I believe and it's end simply got caught and wrapped around the sprocket. I have done this set up before I had the pannier and went over plenty of bumpy patches with no problems. I told my DH about this and his comment was that I didn't have the bungee wrapped "very well". Well no kidding!!!
Thanks for your suggestions and I will play around with different options. One mechanic at the LBS told me, a few weeks ago, that he could mount a U-Lock just about anywhere!