First thing I would do is uninstall the app and see if it stops. It is probably set to disable your cell data somehow. If that is your interest using Smart Actions would be a much better choice.
Or if you want to prove it is an app causing the problem without uninstalling it first, you can boot into Safe Mode. Power the phone completely off, and hit the power button to turn it back on, as soon as you see the Red M logo press the Volume up and down button at the same time until you see "Safe Mode" in the corner of your screen. If your data comes back on fine while in this mode, then you know it was an app.