DL501 7-speed s-tronic gearbox reliability is a sensitive subject. Due to reports of failure and the discussion around them, it is easy to get the impression that it is only a matter of time until they fail, which is not true. Nevertheless I'd advise any potential buyer to research the subject and so buy with his/her eyes open. I have read a lot on the subject and can summarise as follows:
There have been 3 generations of the DL501. The first generation was in 2009 and 2010 cars and (based on reports available on the web) suffers the highest failure rate. I don't know exactly when, but likely during 2011, Audi revised the box to address some of the issues. Then it was revised again sometime around the facelift in 2012, or maybe it was 2013. Maybe there is data to be found on this but I haven't come across it. There have been reports of gearbox problems with all 3 generations, but (again based on reports), the failure rate seems to be much reduced at each generation.
Other than the generation, the key factor in gearbox health is oil. Based on current recommendations the oil should be changes every 38K miles. The first generation box had two oil filters and both were lifetime fit items (not changed at oil service). Based on the engine SSP it was always Audi's intention to delete one of these filters. This was done on the second generation, and the remaining single filter was made a service item.
So my advice to the OP:
This particular car is a 2011 so it probably has a revised gearbox and not the highest risk. But if the gearbox oil service change has not been done to schedule then walk away. It is not worth the risk. If the oil changes were done but no filter changed then that might indicate that it has the first generation box. That makes it an unknown. If the OP is risk adverse, walk away.
Personally I'd recommend seeing a diagnostic scan and in particular of address 02 (gearbox) to see if anything is logged.
