The clogged drain line mentioned above is the usual suspect, and the first thing to troubleshoot. That plastic tray that the AC sits in is designed to catch the condensate that drips out of the AC unit, and channel it into the drain line, which runs between the inner and outer skins, and usually is visible as a small diameter plastic hose sticking through the belly skin in the vicinity of the wheel wells.
Water can also get into this tray in a heavy rain. The tray should have drain holes drilled all around its perimeter. These holes are there to let rain water out, but don't extend into the channels that catch the condensate. Since you are having your leakage during heavy rains, it could be that these holes are either clogged with schmutz, or have been sealed by an overly ambitious caulker--something to check on your next visit top-side.