2006 Audi A6: very strange starting and idling problems

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I have the strangest problem on my 2006 Audi A6: whenever I fill up my tank with gas the car has a very hard time starting. This has happened 3 times in a row now. I run the tank fairly low - to about 1 quarter tank or a little lower but never to empty…then I fill the tank. When I get in the car to start it, the engine just keeps turning over trying to start but will not start. Then I stop trying, let the ignition rest for a bit, and try to start it about 5 minutes later and it starts just fine on the first try. Any ideas what could be causing this?
One thing that has also started happening around the same time as the problem above is that when I’m idling at a stop light, I notice the car may start to idle rougly and seem like it is about to die out.

Any ideas? I am the first and only owner of this car…I take good care of it and am an easy going driver. But I do drive a lot and have about 200,000 miles on it after 7 years.

When you fill the gas tank, do your routinely “top off” the tank? Or, do you stop adding gas after the pump nozzle clicks off the 1st time? If you top off the tank then your evaporation control system could have a problem, the charcoal canister could be overloaded with raw gas. That will cause issues drawing gas from the tank to the engine.

Other possibles are a fuel filter that is filled with gunk restricting flow, or a weak fuel pump.

This could be a co-incidence, that w/200K miles, something unrelated to the fueling is on the fritz.

But it could be something to do w/the venting of the gas tank, as mentioned above. As gasoline is consumed, air must enter the gas tank, otherwise a vapor lock condition prevents gas from going to the engine. And this problem is worse when there is little to no air in the gas tank; ie when the tank is full. A couple of ideas. First, instead of completely filling the tank, try filling it halfway. Does this help? Another thing I’d probably do if this were my car is see if the problem goes away or changes in any way if I left the gas cap slightly loose. The venting would have an alternative path, and could come in through the gas cap point instead of where it is supposed to come, through the evaporative control gadgets. If that fixed the problem, it would confirm the evap systems need some work.

A caution: Leaving the gas cap loose could present a fire hazard, especially in the event of an accident. If you are willing to risk that, one other problem: It could cause the check engine light to come on.

As mentioned above, overfilling the tank is known to damage the evap system, at least w/ some cars.