It is ULPS (Ultra low power state)
It usually happens when CCC disables secondary cards to save power.
Its happened to me (switched off the 5850 and one of the cores on the 5970)
If you want to disable the ULPS it involves some registry editing.
How to do it: http://www.overclock.net/ati/667144-crossfire-disabling-ulps.html
If you want to see if the second card isn't dead, Run the MSi Afterburner.
The software should come with "MSi afterburner On screen display server".
It's like fraps but you can change the settings in MSi afterburner settings display FPS and GPU usage.
It also doesn't use as much system resources.
Run some application (Heaven Benchmark or Crysis warhead etc, etc) and watch if both GPU's are running.
Or you can run MSi Afterbuner in the background, Run furmark or some other application in "Full screen". Quit the application and look on the MSi Afterburner Hardware Monitor to see if the usage has risen or not.