there is a timer in the ECU that advances ignition timing and injector pulse width "post-start" for usually around 30s (could be a minute in the M50tu). One of the signals the ECU sends out goes to the idle stabilizer valve. During warm up, to increase rpms it opens the valve more.
I would use throttle body cleaner and MAF cleaner, and clean the hell out of both.
I would also use a fuel pressure monitor to see what the hell is going on when it starts to sputter. A failing fuel pump or clogged filters could mess things up.
If you dont remember changing your fuel filters in the past year, do it now!
If none of those work, the ECU itself (which controls the injector pulses) could be screwed up or have a bad map somewhere.