Running Compression, and the Battery says "Not Charging". Any Ideas?

Your profile says Mac Pro, but you must mean a Mac Book Pro with the intergrated battery? Try resetting the SMC:

1. Shut down the computer.
2. Plug in the MagSafe power adapter to a power source, connecting it to the Mac if its not already connected.
3. On the built-in keyboard, press the (left side) Shift-Control-Option keys and the power button at the same time.
4. Release all the keys and the power button at the same time.
5. Press the power button to turn on the computer.
   Note: The LED on the MagSafe power adapter may change states or temporarily turn off when you reset the SMC.

From http://support.apple.com/kb/HT3964

I think this is normal behaviour. The AC adapter can only provide 85 watts of power (on 17 inch models) that must be shared among the processor, hard drive, display, etc. For some perspective a MacPro tower (without a display) uses 144 watts sitting idle. ( http://www.anandtech.com/show/3969/apple-mac-pro-mid-2010-review/7 ) You can imagine when the computer is under a load 85 watts is barely sufficient.

If you're going to be doing some serious transcoding or compression (Q-Master, Adobe Media Encoder, mpeg Streamclip) make sure you have some juice to start out with. Connected peripherals (like a bus powered hard drive) are detracting from that 85 watts you have available, so if you need as much battery as possible when compression is over unplug peripherals (hard drives not being used, card readers, phones, etc.), turn off wireless radios (WiFi, BT, 3G/4G USB modems, etc) and lower the display brightness.

I'm not sure why, but it seems I have abused parenthesis in this post. Sorry about that.