I don't know what aircraft you flew on over 3 years ago. The current options from Etihad are Boeing 777 and Airbus A380, and they [don't seem to fly nonstop][1] anymore.

Along the shortest distance -- great circle route -- there aren't many options for an A380 to land and find support equipment mid-route *(shown below).* Refueling [can occur with the passengers on board][2], there is a procedure to be followed, which includes alerting the fire service at the airport to be ready.

If we take **only** the cost of fuel into account, and a 777-200 as a base line, [actually stopping every ~6 hours is more economical][3]. (This doesn't take into account landing fees, accrued cycles*, passenger convenience, etc.) Not just for your flight, but any long-haul flight, the fuel burned to carry the fuel for long distances becomes considerable after a certain range.

Another consideration is which [freedoms of the air][4], say Etihad/UAE, has with say Russia. The second freedom specifically is:

>The right to refuel or carry out maintenance in a foreign country without embarking or disembarking passengers or cargo.

While they are called freedoms, not all country-pairs mutually allow all the freedoms. The specifics are usually not public and are contained in the air service agreement between any 2 nations.

\* Pressurizing and depressurizing, applying the takeoff thrust twice, applying the brakes twice, etc., all increase the maintenance cost.


[![enter image description here][5]][5]  
(gcmap.com)


  [1]: https://flightaware.com/live/findflight?origin=OMAA&destination=KSFO
  [2]: https://aviation.stackexchange.com/q/31197/14897
  [3]: https://aviation.stackexchange.com/a/44496/14897
  [4]: https://en.wikipedia.org/wiki/Freedoms_of_the_air
  [5]: https://i.sstatic.net/Cfq7s.gif