The trunk latched switch can cause this problem. Remove the cover on the deck lid. Look for a connector going to the trunk latch. Disconnect the connector. If the top works, the problem is the trunk latch switch. Seems reverse logic is at play here: if the switch is open, the trunk is latched, the switch is wired so that it opens the circuit to ground when the trunk is latched, the latch keeps the switch open when the deck lid is latched. Problem is that the deck is latched most of the time, therefore the switch lever is depressed. Time causes the activation lever on the switch to bend and ultimately it will no longer operate the switch, thus the switch never opens and sends a signal that the deck lid is not latched.

Confused?

Just disconnect the connector, if the problem goes away, you have found the cause. A simple mercury switch installed so that it is closed when the deck lid is open will solve the problem and will insure the top is inoperative when the deck lid is open.

I checked 4 used latches and they all had the same switch failure.
Good luck.