Get a scan tool on your car and check:
1. Battery volts when you apply your brakes (thinking there is a short in the brake light system, causing the voltage to drop and kill the engine - if the system drops to less than 9 volts, the computer will shut down).
2. Be sure the engine is in closed loop. The IAC won't play into the decel enleanment directly unless you're in closed loop. The IAC responds to idle properly in closed loop.
3. Look for your BLM numbers to be between 110 and 140. If your fueling is out of whack, the numbers will usually peg to the outer or inner boundaries and closed loop fueling control isn't possible. If this is the case, suspect the MAF or O2 sensors and also look for vacuum leaks, especially around the EGR - and check for a "stuck open" EGR.