bhomburg

United doesn't have an outright ban of ESANs on flights longer than eight hours. Instead, they decide this on an individual basis. If you can prove that your animal is trained accordingly and have flown intercontinental flights together without incident in the past, you'll still be able to bring your ESAN on a United TATL or TPAC flight. The agents at the Accessibility Desk apparently are empowered to make these decisions.
I just went through the process with a friend who wanted to fly SFO-FRA (11 hours flight time) on the nonstop flight instead of having to connect in EWR as the UA agent first wanted her to do, citing the new 'no ESANs on flights over 8 hours' rule. She sent in additional documentation and was OK'd for the long flight without any further issues.

Here's the official text from the UA website:
Whether an emotional support or psychiatric service animal is safely capable of traveling on flights eight hours or more in duration will be determined on a case-by-case basis. Passengers may be held responsible for cleaning fees required as a result of any sanitation issues caused by their emotional support or psychiatric service animal’s travel. United will consider all relevant information, including information from the required documentation, when determining whether an emotional support animal or psychiatric service animal may safely travel in the aircraft cabin on the passenger’s itinerary.