Intermittent Idle problem Audi A3 1.6

[A3 puzzler]

My Audi A3 1.6 (1999) has an intermittent idle problem. When it plays up, the revs hunt from between 1000-1300rpm and this can be felt as a surging when driving slowly or gearing down. When I feel the cable pulley at the throttle body I can feel it pulling at the throttle cable up and down like a boy racer at the lights.
The diagnostics computer has not reported any faults except for a throttle sensor fault which no longer shows.
So far, I have replaced the throttle body, replaced the timing belt, taken it in for a full service, done a default reset and each time, the problem has gone away only to return weeks later.
There is no correlation with the temperature of the engine but what I have noticed is that if it is OK and then switched off for over 10minutes before being restarted, the problem comes back. The engine runs with a good even power output over the rev range and is otherwise perfect.
Another clue is that if I rev the engine up to 5000rpm for a couple of seconds, the engine will settle down, and rev evenly at a very steady 800rpm for anything between 10 minutes and a day.
Could this be the Mass airflow sensor...any ideas please?

[kite]

Look for an air leak, sounds like unmetered air is getting to the
engine.
Look for split pipes or tiny holes.

[A3 puzzler]

Thanks for the suggestion, I will take another look - I have just replaced pipes handling air to the throttle body and everything else that looks a bit 'past it'.
Do you really think that this is consistent with a fault that can present itself hot or cold stay for days and then disappear for days? I would expect an intermittent air leak to occur either at a particular temperature ( as parts expand) or with mechanical disturbance. I have tried rocking components around to see if it makes any difference ( it does not) and as I have said, the fault can occur hot or cold.
What do you think of my other suspects: idle stabiliser, temperature sensor, O2 sensor, Ground to the ECU- or other ECU fault that would not show up on diagnostic computer?

[kite]

It could be the MAF, but how long are you going to throw parts at it !!

[A3 puzzler]

I don't know how much longer I am going to try to sort this out. I have a 41 year old Austin that is quite capable of ticking over reliably without a hint of a computer!
I really like this Audi but the whole experience is ruined by this problem ...and it does not even show up on the diagnostics computer.
I was hoping that someone with some expertise would be able to diagnose from the information that I have given the most likely cause...I do not have much practical experience, I just understand some of the principles.

...So, if the MAF is faulty could that cause the revs to rise and fall as described?
What does the fact that I can feel this rise and fall of revs even when I am gearing down mean?...is the idle management designed to carry on working in the background all the time or is there a switch?
Frustratingly, I have not been able to find anyone with a sufficiently analytical mind to be able to work this out for me.

[kite]

Just seen your in London.
Try sending a PM to adamss24, he's a member on and I think he has a garage...

[A3 puzzler]

Thanks...I got my A3 scanned again this weekend and this time instead of no faults it came up with too many! The MAF, the temperature sensor,the throttle body ( I think it was the idle stabilisation)...they all came up. I have got the faults cleared as I do not believe it can be all of these things at the same time and plan to drive around for a few days before getting it scanned again to see if just one fault comes up. - I am going to presume that the one that comes up is the culprit.

[Crasher]

You have done the right thing having it cleared and trying it again after a few days driving. Ohh and about the Austin, I agree with what you say but the Audi could probably run on the unburnt hydrocarbons coming out of the Austin’s tailpipe.