Hi,

not sure about the 4.4 engine but on mine 3.0i I had similar issue (would start fine and die once rpm started to go down, pressing on gas pedal would keep it alive until it warmed up). I narrowed it down to ICV not working as expected. I took it out cleaned it made sure it flaps when shaken and it fixed the problem.

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2004 x5 3.0i AT.