I'm following these instructions to use my mid-2009 MacBook Pro in clamshell mode with a Bluetooth keyboard and trackpad. The keyboard and trackpad are paired with the computer and I've got the external display hooked up, but the computer is going to sleep when I shut the lid. I have Allow Bluetooth devices to wake this computer checked in System Preferences, so I can hit some keys to wake the computer while it's closed. It wakes up and shows me the lock screen, where I start typing my password... only to have the computer go right back to sleep after a second or two.
Why won't it stay awake?
Clamshell mode behaved properly when I was using a USB keyboard.
I'm currently using NoSleep to work around this problem, but I'd like to know the root cause.

[clamshell-mode]tag. – Abby T. Miller♦ Mar 29 '12 at 14:49