Bad run with rechargeables this year!

Like the Subject says, I've spent a fortune on new rechargeables to replace those which have died. My question is, is keeping the devices on charge 24/7 going to "cook" the rechargeables?

Here's a summary:

1M Candela torch- 12 months old. Battery lost its power to keep a charge while on load. Battery is a sealed Lead-Acid 6V 4.5 AH. I keep it on charge 24/7 using the supplier's charger.

Ryobi Cordless Drill- 24 months old. Battery pack is made up of 12 individual 1.2V cells in series (14.4V). All batteries ended up with 0V across each cell and it looks like each one started expanding (heat?). Drill was on charge 24/7. Bought a new drill for 70% of the cost of the replacement battery pack)

Ryobi Cordless Drill- 6 years old. 2.4V battery drill with 2x 1.2V cells. The cells started "leaking" a fungus-looking substance from each end. Drill was on charge 24/7. Replace batteries with new cells. Note supplier's charger is 4.5V AC (yes AC! Drill has resistive wire and diode in series with charger input and battery terminal).

Looks like charging a rechargeable device 24/7 kills the batteries, probably due to excessive heat. What's your suggestion?

Low cost chargers do not have automatic cutoffs. Read the manuals and see if they say to remove the charger after a certain time period. In general, overcharging does degrade the batteries.