I've had my Rezound for about a month. The battery life ALWAYS sucked, but mine got worse, too. My battery issues are solved now, and here's how I did it. I got rid of things like "Juice Defender" and "Tasker", and I installed "LTE Switch" to turn off 4G. Let me tell you, since doing it, I don't miss using 4G AT ALL! The trade-off I got in battery life was well worth it. Like you, my battery drain was easily 3-5% every few minutes, even when the screen was off and the phone was "idle". I was lucky to get 5 hours of life. Now, with 4G switched off, I get (easily) a full day. For instance, today, I took the phone off the charger at 11am.. since then, I've been using it a lot today (medium to heavy use), texting, customizing my page layouts and widgets, some internet use, downloading on the market, opening apps, the display at 30-35% brightness, etc.. it is now 10pm, and the battery is at 10% (almost 12 hours of use, and just enough juice left before putting it back on the charger before bed!). Yes, this is all with the standard battery.
With the Mugen 1900mAh Slim Extended Battery coming out in a few days (which should fit the standard battery door, and still allow me to use my protective case), I should be sittin' pretty