It's been quite a while, but, the beeping issue finally seems to be resolved. The issue continued intermittently for about a year. I brought it in to the dealership's service dept. at least six times and they kept diagnosing various minor issues. Then the hydraulics system ran dry, but, they determined it was not leaking. FINALLY, the system just shut down (thank the lord for showing mercy). They found that the pump was bad, so, they installed a new one plus new cylinders . Then it got fun because the original control unit doesn't interface with the newer version pump, so, throw in a new control module. In the end, two & a half weeks plus $6,000.00 = fully functional top with no beep.... well, at least she waited until the next day before it started again. At that point I blew a gasket, slammed on the brakes and pulled on the side of the road. I popped the top, ran the 'up' cycle to reset it, yanked the handle extremely hard and latched it down.
It's been three months now and no more beeping.
By the way, did I mention just how happy I am that I bought the $2,000 extended warranty when I got her? So far over $10K in covered repairs. Dispite that, of all the cars I have owned, this is my favorite. Even so, I wasn't willing to chance it once the wty runs out. I was actually planning on selling her before the warranty ran out, BUT, Chrysler must really know how much I love her. They have offered me another 5 years / 75,000 miles. Didn't think twice, just signed on the dotted line.
Looking forward to a lot more road trips!!