I've used my MBA to drive a 1920x1080 24" display doing all kinds of things graphic intensive, like watching HD video, and never had my 13" MBA kernel panic in clamshell mode. Sure the fans start running fast but I've never experienced a kernel panic. I'm inclined to believe there may be something wrong hardware-wise if you are getting kernel panics. I use the Bookarc now but only very recently, up until then it just sat on my desk.
Kernel panic you will usually see a grey screen asking you to restart your computer. Just do a google search for "osx kernel panic" and you will come up with lots of information.
I'd run iStatPro or smcfancontrol to find out what the CPU temps are before the kernel panics occur. If the CPU is hitting 90C or higher in clamshell mode, I'd suggest running with the screen open and sticking a fridge magnet near the headphone port. This fools the computer into thinking the lid is closed and it's in clamshell mode.