I don't know that phone, but my best guess would be that some app is turning the data on.
To assist in identifying the app, you could use an app which lets you view your apps' permissions. Many security apps can do this, as can Addons Detector. At a guess apps with the permissions CHANGE_NETWORK_STATE or MODIFY_PHONE_STATE might be able to do this (just looking at what permissions my own apps have), so that might give you a starting point. I don't think that an app could do this without one of these permissions.
Note that an app having these permissions does not necessarily mean it's the culprit - I have 4 with the first of these permissions, 2 with the second, and don't have this problem. Also I might be wrong about what's going on here, this is just a guess.