Are you using the new '06 Kicker ZX series? I had the same exact problem with a 06 zx700.5 and the Rainbow SLC. The difference is that I am trying to tap into a factory bose system, so things are a little more complicated.
Since you are running an aftermarket HU, the signal SHOULD be fine. Do you have access to a multimeter? First check your impedance at the amp terminal to make sure you are seeing 4-ohm (or around there). Next check your remote turn on voltage, when the amp is powered, it should stay above 12V all the time.
I suggest you bring it to a shop. I tried to diagnosis thing myself, end up blowing the SLC and the Kicker amp. First it was cutting in an out, just like what yours is doing, the LED switched between red and green. And later it stayed red, and wouldn't get out. So yeah, I am pretty pissed off. Amp is under warranty by onlinecarstereo.com, they say it will take about 4 week to get it back to me. 6spcoupe is looking at the SLC to see if he can replace it for me. But yeah, when I get all my gear back. I'll definately bring it to a shop. **** with an Arsenal 12 all nicely done in a fiberglass box and no power or speaker!!