Most big fans don't run at even 5 volts, let alone start up on power-on. 6 volts is the safest IMO, but some big fans recommend 8-13 volts for operation. They don't change the voltage internally to get a certain RPM at 12 volts, it has to do with increasing/reducing the 'winds' (wire) on the armatures (thats what they're called in, umm, non-brushless motors).
When you run a 12 volt fan below 5 volts, it stops, but its still using energy. That energy is basicly frying your fan's electronics, if not all at once. The following solution may/may not work, since I haven't delt with diodes before. If you ran a ~6 volt Zener diode between the power regilator and the fan, it would let all voltages above 6 volts pass to the fan, but cut the power below 6 volts. Zener diodes are usually used as a surge bypass (normally open connection), and I don't know if they'd heat up or take the prolonged periods of normally closed operation.
Other than that, you'd need new 10k ohm pots that have an off switch on the low-ohm side (hard to find, if they even make them), get a new IC and redesign the whole circut, or rig a switch rated for at least 3 amps/14 volts/20 watts and put it between the power regulator and it's respective fan output. You'd have to manually switch it off, but its the easiest in my opinion.
Based partly on how lots of Nexus's have fan channels die as well as how my Nexus has a minimum of at least 7.7v (too high for me), as well as how it whines at low voltages - I'm actually going to gut my Nexus and make a few LM317 circuits. I'll even one for the LEDs, since the Nexus IC controls them too. I'll be in complete control of the voltages, and they are known to be reliable. I can also swap in a LM350 and get a 3 amp channel - enough for even 2-4 big deltas.