928 rough idle/drivability problem
 

I own a fairly pristine '89 S4 with manual transmission. In the past it always struggled to idle after the battery was disconnected for a time, and I was told the computer needed to "relearn" all the idle settings. Most recently, after the car sat without a battery for a month or so, the car is still stumbling and struggling to idle and I have had 3 occasions where the car suddenly started running as if it were firing only a few cylinders- it sounded horrible and had no power. Surprisingly, I turned off the car, waited a bit, started it up and it was fine.
As I said, however, it subsequently happened two more times.
Does this make any sense to anyone???

When the ECU is adapting the idle after a reset it will alter the idle speed but it should not struggle. You may want to check for air or vacuum leaks and have your MAF checked if you don't know the history and how many miles are on it.
Does it sound like it's running on 4 cylinders when this happens? It may be the ignition protection relay, it's on the same cradle as the ECUs, check if any LEDs are lit up when it misbehaves.

Thanks for the insight
The idle searching seems to be a separate problem from the episodic "running on 4-cylinder" problem but I can't help but believe they are related.
I could not find any vacuum leaks but I'll give another look....