That's been my experience. Your mileage may vary. Let me explain... or expound...Nonsense!
Ours were always connected to the inverters/chargers and had a life span between 3 and 4 years.
Now with our solar system we'll get even more life out of them.
donP
As mentioned, if the battery is weak/old, it will continually take a charge, because it continually loses it. In this way, it's 'on' 24/7. Also, if a person doesn't check and add water to the battery on a regular basis, that will make it get old quick as well.
With the invertor, we had astronomical electricity bills of 6000 pesos a month. Without it (we have good service now), it's down to 1500-2000 pesos as a regular bill.