bet they are closing to the same point they should drop to when put the top down, right?
cause:
Bad microswitch for top (located in catch housing between the motion sensor eyes). could be as simple as just cleaning it, resoldering the contact wires as they are known to crack or replacing entire switch. Try re-closing the latch for the convertible top a few times to get it to activate.
See part #6 in this link:
http://dcauto.gotdns.com/illustration/index/483702590?class=illo_title
If you need to replace, it's a pretty simple DIY.... you'll need a T-30 bit to remove the 2 screws hidden behind the "eyes". Alos, shop the price out at Sunset or Suncoast s well.
good luck