Sounds like it's possible that the cold start valve is closing too soon.
There's a temperature sensor that tells it (basically another fuel injector)
when to close as the car warms up.  It could be that the sensor is going bad
and its temp range has changed...or it is possible, but not probable that
the cold start valve is not providing enough fuel flow.  The reason I don't
think that's the problem is that the car starts properly, and only begins to
exhibit problems after the engine is running.

The other things to look at are whether the fuel filter is dirty, is the
fuel pump working at full pressure, and is the fuel distributor in the CIS
system dirty...and not providing enough fuel.

However...since the car starts properly...and runs OK when it's warmed up,
I'd look for a bad sensor.  I haven't had a CIS equipped car for years and
cannot remember how or where they measure the engine temperature.  It might
be electronic, but it could be something more mechanical, with a simple
bimetal type, thermal sensor.

There are books on CIS, Rennlist, Pelican Parts articles, etc.

Hope this helps.  Maybe someone else reading this will lend a hand.