Kelly -
I have a Bushnell, and also turn it on when I rack a shell and then turn it off when I unload. I can get 4-5 years out of a battery when using it in that manner, maybe more, but I usually change the battery before risking it.
I have no scientific data to indicate how long a new battery can last, and obviously turning it on/off will draw more power than just leaving it on, but I know I can get more than 500hrs from my Bushnell. In 2016, at the end of turkey season (end of May) I unknowingly left the scope on and didn't touch it again until mid-November when I got it out for deer. The dot was weak but still visible - after being left on continuously for ~ 5.5 months or ~ 4000 hrs of continuous use. I changed the battery but was damn impressed - and because it's a watch battery, the sight will progressively get weaker and tell you to change the battery, it typically just won't outright die.