battery backup is poor

The Phone Radio is using up a substantial amount of battery, which could be due to poor or fluctuating cell signal strength. As previously suggested, show us the Cell Signal Strength graph.
 
Yep, it's your cell signal. See how the battery curve is steepest where the phone signal is fluctuating into the lower area?
 
You don't have to remove the SIM -- just turn on Airplane Mode. You can always turn wi-fi back on in Airplane Mode.