Now I've had starting problems before (this is a jeep), but I haven't a clue on this one:

I turn the ignition when the engine is cold and the the starter fires away and she roars to life. I turn the ignition when she's been warmed up by at least a short drive and it sounds like everything is fine, but as soon as I let go of the ignition the engine dies.

What gives?

it sounds like the B+ latch relay, check this link. I helped a guy out that was having problems by removing my relay and it would only keep running when the ignition was in the start position, turned out to be his problem.
http://autorepair.about.com/library/illustrations/bl920lib.htm

Thanks for the start, I'll look into it.

What is the function of the B+ latch relay?