There could be a rusted out area or the seals around the vents could be leaking if the drains are clogged. 1st thing you need to do is determine where the water is coming in at.

I cleaned mine by pulling both fenders & both under dash vents/heater core & used compressed air & long bottle cleaning brushes(taped to a wood dowel rod) from the cowl vent in, from the drains behind the fenders into the cowl & up through the interior vent openings.
 
I blew 32 years worth of crap outta there & thought it would never stop coming out. If you have rusted areas you will find them with everything out from under the dash. Check the vent seals for cracks but they're usually fine.
 
After the cowl was clean & dry I jacked up each side of the car one at a time & poured black Rust Oleum paint in the cowl till it ran out the drains & let it dry. I also used spray cans & stuck my hand up the vent holes & sprayed in every direction.

Thanks for the reply.  I have a suspicion the wiper posts may be leaking as well.  How did you go about sealing those up?  Do you have to do that from the inside?  Thanks!