Can’t say… maybe you got a faulty battery? That hasn’t been my experience when using ERG.
I’m not saying battery life would be indefinite when using ERG, but I go months between charging when primarily using ERG, and I do wake them up for each ride as I like to shift between chain rings for standing efforts.
Edit to add: maybe your system isn’t going to sleep, which will obviously drain the battery over time. You can tell if they are asleep or not by clicking a shifter button. If you click it once and nothing happens, it’s because the system is asleep.
If it IS asleep, you have to click twice for the first shift as the first click wakes up the system.