The reason why it takes so long during the intial IRS alignment is because the IRS has to determine the true north. It does this by sensing the rotation of the earth, thus as you go higher in latitude, it takes longer. If you exceed a certain latitude, you wouldn't be able to align the IRS at all ! The old gyro based INS does pretty must the same but the difference you have to get the gyro up to speed in the first place and it's restricted by it's gimbal travel.
Determining the true north is only half the problem. The other part of the IRS are the accelerometers. They basically worked on the good-ole pendulum principle to determine the rate and direction of travel. These accelerometers are the ones that are giving us most of the problems. Over time, they can give false readings thus causing 'drift'.
During a quick alignment, what we are doing is simply 'reset' the accelerometer drift to zero.
Hope this short explaination helps you understand better.
HS