Ford: Intermittent Starting Diffficulty-Ford ExplorerEB 2000

My Ford Explorer EB 2000, with 39K miles on it has an unpredictable
problem with starting. Sometimes when I try to start after it has
been parked for about 12 hours or over, the engine starts but then
immediately stalls as the ignition switch moves from the start
position but if I press the gas pedal to raise the RPM to about 3000
or more (and keep it there for 15-30 seconds) before the engine
stalls, then the engine does not stall.

The problem is sporadic, the car could be parked for several day at a
time and it would start right away and it could be parked for just
10-12 hours and it would have this problem. Appears to be something
related to fuel delivery to the engine that somehow gets depleted if
parked for a while.

I am wondering if this is a sign of a serious trouble to come and as
to what could be wrong, since the problem is not reproducible at will
it will be hard to diagnose and fix.

Any ideas?.

Thanks, in adavane.

Matt