If watching the charge level with the display turned on implicates you're using the device while charging, the explanation might be easy -- if the following example somehow matches:
Assuming you're charging via USB from a computer/laptop/other-USB-source (i.e. not the wall-plugged charger). According to the USB specifications, this provides a charging power of 500 mA (USB 2.0) or at maximum 900 mA (USB 3.0), as you can read e.g. in this Wikipedia article. Now taking the Samsung Galaxy S3 (as we've got some reference data for this device, see my answer here), and let's play some numbers:
- You're recording some video. This uses 1683 mW.
- You're downloading something via UMTS (3G): 1074 mW
- You're using the camera: 1460 mW
- You tethered your laptop to the phone, and download something: 1254 mW
All these things with the screen off! So you've got to add another ~800 mW for the screen (567 mW to 1568 mW, depending on brightness and colors).
In each example (and I can easily construct several more like that combining some facts, like "Bluetooth download (487 mW) plus average display (800 mW) → 1287 mW), your device uses more juice than the USB power source can provide. Consequently, your phone -- although connected to an external power source -- DIScharges. This would be the case even when performing no actions, just having the display turned to max with a non-black (but rather white/colorful) picture: 1568 mW > 900 mW.
So, rule of thumb: when charging via USB, keep the display off; USB 2.0 cannot even provide enough juice for a fully dimmed display (567 mW > 500 mW), in case of the S3 (it might be slightly different for your device: the Motorola Milestone e.g. needs just 310 mW for a fully dimmed display).