the specs for 2001+ are 656-984 ohms for the pulsar (red to white, disconnected from cdi) , so you're probably good there.
the cdi stator for the 2001+ are around 624-936 ohms (green to brown, again, disconnected).
(i don't have the specs for the cdi source coil/stator. edit: disregard).
you sure you measuring the cdi power not the 12v stator?
on the older tw's the cdi power is ~430 ohms across, and the 12v coils are ~.5 ohms to ground
pay attention to your meter readout, the decimal place, the units (ohms, k-ohms, etc).
if you can verfy spark or not when it dies that will help, as it could be a carb/fuel supply/vac lock issue as well.
electrical is often intermittant so if you can immediately meter when it dies that will help.
cooling spray from electronics store can help pinpoint.
the cdi is far from engine but it is downstream from it, and under your leg, above the muffler pipe, and generates it's own heat... if it cacks out , and you can immediatly spray it with cooling stuff....
i would also suspect the spark coil because that definatly gets hot. cheaper also.
there are manuals on this site, just search. "01 and newer supplement", also somebody posts custom coloured diagrams here as well.
try a third plug; and also swap pugs when it dies.
you are "lucky" in that your bike will start, so you can wiggle wires while running, heat components up with a hair dryer, etc.
good luck, have fun...