How is your Protein Skimmer working? How often are you emptying the Skimmer?
How new is the Live Rock? Was it cured?
I am still in belief that the tank is going through mini-cycles every time you remove the filter, then put it back on, then remove it again. I think that there is a certain amount of ammonias and dissolved organics that get mixed into the system (from the changing between filter and no filter), and bacteria die-off as a result of this.
Every time you use the carbon it is absorbing these organics and what not, just as a carbon filter on a tap system makes your water taste better.
I think you should run carbon almost religously, but make sure you clean the carbon out religously as well.