If you're not on a 5C/5s, turn wifi off when you're not using it, and cellular data off when you're not using it.
Until they refine it, mutipath tcp is not so hot for ip5 and earlier. There also seems to be a Facebook secure login loop that occurs in background, despite whether you have an account registered in settings / app installed. I have contacted the dev with the particular app I am using to check my connections, but it looks like my devices are trying to login to Facebook a few times every minute.
I've confirmed and replicated it on freshly restored devices on genuine builds of 6 and 7.. without any user interaction ios contacts facebook secure login, establishes a connection and without the right credentials it gets the boot.
Device loops and retries less than 30 seconds later.
As a result CPU load on A5 increases by 15-20% during these times. Wifi never goes into low power mode and over 3G the persistent establishment of connection leads to further uptime and drain.
If you have bad coverage you may have an increase in the number of retries, leading to greater demand on radio and CPU.
If it is not the monitoring app doing it itself, unless apple investigate and recognise its real potential to waste cycles, we are all stuck with it. I've read in several places about the Facebook app doing a lot in the background (here's one
http://www.tuaw.com/2013/06/04/developer-suspects-facebook-app-is-behind-iphone-battery-drain/ )
If what I've seemed to have found is consistent with that, then ios is the culprit, not the app.