No fan runs on a swept voltage range over 30 seconds.. That's the response of the Xbox fan driver itself... Probably as the system powers up and heats up.
First off he needs to use fans that run directly off 5Vs, the idea of using a 9V battery to supply the fans is ludicrous from the start. When the circuit loses the 3.3 V signal it turns on for a set time, you need a 555 for that for the one shot, but the one posted so far does not function.
The hardest part of this I see is finding fans that run well off 5V directly. ALL PC fans I have ever seen use 12 volts, and require over 5 volts to start. (hence the 5.4 to 11.8V ramp seen)
The system starts, starts the fans off on low. 5.4V, ramps up to 11.8 as the system generates heat. Pretty simple.
The only other option I see is using a giant capactior with a diode to prevent it from discharging into the supply from the 12V supply to a 12V fan, when the 3.3V signal is lost it'll trigger a transistor from the capacitor to the fan turning it on, but that will only be a for a few seconds unless you spend more money on super caps that are worth more than this entire project.