I think the problem is in or around the ignition switch, and I think the 12V feed to the coil of the PCM Power Relay, which should be hot in Start or Run, is only hot in Start at those times when the engine quits - i.e. it's no longer hot in Run. That should be easy to check at fuse # 9, rated at 10amps, located in the passenger compartment fuse panel - well, it will be easy to check if the fuse has the little access holes in the plastic body which serve as test points through which one can probe for voltage - some fuses have them and some don't. If the fuse has no access holes then look at the other fuses to see if you have another 10 amp fuse which does, and swap them.
The fuse itself will be good (otherwise the engine wouldn't start) but when the engine starts then quits as the key is released, leave the key where it is - in the 'Run' position - and check for voltage at fuse 9 using either a multimeter or a 12V test lamp, and I reckon there's a high chance you'll find the voltage is missing. One probe to ground, and probe through the little access holes in the fuse with the other. If you don't have a fuse with test points then just unplug it and probe into one leg of the now-empty fuse socket, then the other - one of them should have 12V.
If you do find the 12V is missing then it might simply be worn contacts, in which case a new switch would be required, or it might be a linking bar - an actuator - between lock cylinder and switch which is out of alignment - I don't know how the Windstar ignition switch is physically arranged.
Next time it happens though, check for 12V at fuse 9 and I'd be very surprised if it isn't missing.