Had the same problem on my 560 SEL. In mine, it was a leakdown by two (not one) injectors. I replaced them all.
If you have room to climb below the car, you might want to consider replacing the accumulator first - it's not very expensive, and the main duty is to keep the fuel line pressurized while the car is warm but turned off.
For the injector job, search this board - I have given a description on how to do it. You'd want to do all the seals, insulators, etc while you are it - they're cheap too, so no biggie. Your biggest cost will be the injectors. Nice DIY project.
1989 560 SEL (black/black)
2001 Audi TT Roadster (silver/grey)