I believe there is also an issue where the batteries corrode and destroy the circut board inside causing a battery draining short. Do a search on sirens.

 

You are correct. The corrosion from the failed batteries have caused havoc with the circuit board in the siren module. My question more specifically was prior to total failure and acid leakage from the batteries, are they being recharged and what effect might failing/old NI-MH batteries have on car battery drain. My experience with NI-MH batteries is that as the battery ages, its ability to hold a charge decreases which results in more frequent recharging.