86 5kt dying...help!

[Rokas Reipa]

Hello all..Haven't written in a while, because seemingly there wasn't much
to complain about but with these cars, something major always pops up..So
here goes: Subject is a 1986 5000CS Turbo(non-q) with a 3sp automatic. Cold
starts are fine, car fast-idles at around 1200 or so, eventually settles
down to 800-900 or so. Drive it around for around 20-30 miles, at 50-90mph,
city/highway. Park it, go inside, come out 20 minutes later and car WILL NOT
START. Most times, it won't even catch. In the off-chance that it catches,
any sort of idle stabilization is non-existent because I have to nurse it
with the gas or it stalls. If it doesn't catch the first time, it takes a
while before it starts and when it finally catches, again I have to nurse
it. At this point, idle is very low; when stationary, the car almost always
stalls. At stoplights, I have to rev it in neutral to prevent this. Twice
now it has stalled on me in a busy intersection. If it stalls, it sometimes
restarts on the first try and sometimes it takes a while. This low-idle
situation takes about 5 minutes or so to disappear; revving the piss out of
it in neutral seems to shorten that time. What is the problem? Vacuum leak?
Some hose leaking somewhere? This problem is driving me insane and is
extremely embarassing! Please help! Thanks,

Rokas
86 5kcst