What would cause intermitent "too lean" codes - computer stepping mixture down?

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Hi, I have a 2003 2.5L gas Freelander that a month or so ago when started exhibiting intermittent severe losses of power. I have an inexpensive Blue Tooth code reader that I use with the Torque app on my smart phone. Various fault codes come up equating to one or both banks "too lean" then various misfires. When started from cold it starts up as normal for the first 5 to 10 seconds (must be starting on some sort of predefined rich starting mixture and control) then when it would normally back down to idle rpm it begins to run very rough and often dies. Pressing the accelerator during this drop off has little or no effect. You can hear the extra air flow but the rpms don't pick up and instead it either coughs and jumps or just dies. At this point if you try starting it multiple times and keep the rpms up during and after the 5 – 10 second startup cycle it will eventually "clear itself" and run pretty normal - for a while. Then using my code reader and having my son ride along and monitor some of the engine parameters I've been able to test drive it and make a few observations: When it's running well the short term fuel trim on both banks is up around 27%. Then for some reason these trims start stepping down (he can watch them on a graph and they tend to move together in what looks like a stair step pattern) and eventually go to zero. While this is happening the engine loses power and all but dies. Keeping the rpms up can prevent or reverse the step down in trim and roughness. So it seems that higher rpms help the situation but I'm not sure. Also, once the engine is warmed up, shutting it off and restarting always brings it back to normal for at least the first 5 – 10 seconds and often it will continue to run fine for up to 10 minutes or more (as long as it's not just at idle). I don't know which is the cause and which is the effect. The engine control unit seems to be stepping the fuel mixture down to the point that it's too lean to even run but I don't know what the root cause is. And keeping the rpms up either mitigates the underlying root cause or puts the engine control unit in some other control "mode" that automatically calls for a richer mixture. I've tested the fuel pressure, looked at the spark plugs, monitored the O2 sensors, cleaned and monitored the mass airflow sensor, looked for vacuum leaks etc. but I'm not sure what to try next. Oh and by the way, I have had some trouble with the butterfly valves and motors in the plastic part of the intake manifold so they could be acting up again but I'm assuming they couldn't cause these more serious symptoms? Anyone have any ideas?