Same thing was happening to me. I had an app killer running that I uninstalled just to see how much it would drain my battery. I tested it first by uninstalling the app killer and ran my phone as normal for 2 days. I never noticed any real change until I installed WWF and I saw a dramatic increase in battery consumption.
I highly recommend using a task killer such as ATK(advance task killer) from the market. Unless you want constant notifications (I do not) for your turn. You can also disable the updates and the notifications in the WWF settings menu.
LG Optimus S // ROOT and flashed with Reborn ROM (overclocked to 825MHz)