Welcome to the forums... battery life on smartphones is not great to be honest.
Any weak signal will cause battery loss. When a phone/tablet detects a weak signal, it will send more power to the radio to boost its ability to connect to that signal (I think).
Similarly any drop from 4G->3G will cause the phone/tablet to look for a 4G connection, also causing battery drain for sure. The same is true for WiFi -- if the connection gets dropped, the phone/tablet will work a little harder to find it.
Best bet is to use something like Tasker and/or some widgets to really control when any battery draining activity is taking place.
Battery draining activities include:
-The screen being on
-3G/4G
-WiFi
-Bluetooth
-Background data sync
-Any large data transfer or frequent screen redrawing
(eg the surfing the web with the browser)
You might want to check out the sub-forum for your phone -
Sony Ericsson Xperia Neo V - Android Forums as other users will be able to give you the best hints and tips on getting the most out of your phone!
Hope you find this place useful!