Since almost a week, my xperia P drains the battery at night. It starts around 1 a clock when the screen turns on by itself. Although there is a screen timeout configured of 30 seconds, the screen never goes off again. I am still running 2.3.7 (Build number 6.0.B.3.184) as pc companion tells me this this the latest software. (I live in Belgium)
Try to update with SUS: http://www.sonymobile.com/gb/tools/update-service/ Have you activated your Battery Saver,or something like that,which does between 1 to 5 in the night stop connections?
It's a strange problem for me. Me too using Xperia P and running on ICS. Kill all the running applications before you go to sleep.