I also remember a trip in the mid 80's when a tropical depression came in and sat on Cozumel for a week with a solid 24/7 rain. The pool at La Perla (now Blue Angel) overflowed and the streets were like rivers. I extended my stay to try to get on the other side of it, but I ended up leaving in the rain.
Please keep in mind that us "old timers" are referring to very infrequent events. Mid 80s, 1995, 2004!
Dave