Short update, I went back to the original Nintendo battery and it lasts between 2 and 3 hours of playing Pokémon with the internet connection on. Not ideal but WAY BETTER than the ZedLabz battery.
THIS IS THE POST I HAVE BEEN LOOKING FOR!
I have the same exact issue as the original poster (o3DS from 2011, battery dies at 50%). However, in my case the original battery lasted around 2 or 3 hours and I decided to change it, also for a...