I buy a lot of those little timers for my business. They get pretty heavy use, maybe running timers for about 6 hours per day. They don't last anywhere near decades for us.
Anyway, my insight is simply that some of them turn off the LCD after a while of non-use, and some of them keep it on indefinitely. Maybe that explains the difference between your two experiences.
The timer I had never turned off the LCD. I found it in early elementary school and the same battery was still going strong when I got married in my late 20s. So it lasted 15+ years on a single AAA battery.
I had the same exp. One I bought in the mid 90s. That original battery that came with it lasted nearly 10 years. Then another 5 with the new battery. I retired it when the plastic casing came apart. The LCD never turned off. That thing was a tank.
The newer ones I am lucky to get a year out of the battery. Even using the on/off switch.
I've noticed something similar with remote controls. Receivers, CD players, DVD players, Blu-ray players, TVs, cable boxes...almost every one I've ever bought came with batteries that lasted for many years. Sometimes longer than the device the remote controlled.
Then, when the remote needs new batteries and I put in the batteries sold in US stores they would last a year or two.
The batteries that came with these devices were brands I'd never heard of and never seen at any store in the US. Usually they had lots of Japanese-looking writing on them and little English except for the brand name.
1) The OEM battery was probably fresher than the one that wound its way through retail distribution and then sat in a drawer at your house for longer than you realize
2) By the time you have to replace a battery, your remote's PCB has had time to adsorb water and contaminants from the air, get soda spilled on it, etc and is going to have higher leakage. It will then always draw more current in standby.
Anyway, my insight is simply that some of them turn off the LCD after a while of non-use, and some of them keep it on indefinitely. Maybe that explains the difference between your two experiences.