Could be the Coolant Temperature Sender which controls the enrichment of the fuel mixture. When they become faulty it runs too rich to the point of cutting out or not starting. I've had two fail on me in 3 years.
My wifes current daily driver is also a 2.8Q A6.
Look at the back of the engine in the middle sort of under the "Y" suction pump and you will see the sensor tapped into the coolant pipe. Check it has the green plastic plug molding not the earlier black one. Audi redesigned them because they were a known fault and even went to the trouble of colour coding the redesigned part so you can see at a glance if it's been changed.
Pelican sells them here. Even if this isn't the immediate cause of your problems they should still be changed to the updated part as a matter of course.
Coolant Temperature Switches near the bottom of this page;
2000 Audi A6 Quattro Base Sedan - Switches, Motors, Relays, Fuses & Wiring - Page 2