I have a 2011 4.6 (same engine and transmission) and had the same issue about 18 months ago, right at about 75k miles. I'd slow my car to a stop sign and the transmission would do a hard 2nd-to-1st drop down when either finally stopping or rolling forward on the gas.
Did some research here and elsewhere and the consensus was that the ZF 6HP26 is pretty robust and used in a lot of Euro high end vehicles. The issue seemed to lie with the concept of "Sealed for Life" fluid. While Hyundai does not even have a
dipstick, there is also no service recommendation for the transmission fluid, only "Check". How does one do that with no
dipstick??? When used in BMW, Jaguar, Land Rover and others, this was not the case. Wisdom seemed to indicate that this fluid should be changed regularly. That is what I chose to do and the issue was resolved.
What I did was a trans fluid exchange at a local Goodyear center that I trust, using a Robinair Fluid Exchanger. I chose not to drop the pan (somewhat for cost and somewhat that I didn't feel the risk warranted it) and this may have been a bad move, not replacing the pan means the same filter is in there as new. We'll see if I turn out to be a goat on that one.
I used 12 quarts of fluid through the transmission cooling lines. I know that it doesn't get 100% of the fluid, but certainly was enough to notice the difference and solve the issue. Another choice I made was to use ZF Lifeguard6 fluid instead of the Hyundai brand. Able to find it from California Transmission Supply Company for $200 for a case of 12. ($16.66 / qt rather than Hyundai $$$$). Also, the owner's manual states that the 4.6 transmission can use any ATF M 1375.4 compliant fluid. HOWEVER, when you dig into lots of Synthetic or conventional ATF maker's documentation, they almost all have exceptions for this transmission. I stuck with the ZF fluid. They made it. They should know.
YMMV, but I plan on keeping the car for the foreseeable future and it seemed like a worthwhile investment.
