In order to maintain your green card / resident status you cannot be out of the country for more than 6 months a year otherwise you can jeapordize your resident status. However, you can pay a fee and file some paperwork with immigration explaining that you still reside in the US but are working abroad and may be out of the country for more than 6 months, but it is important for you to file the appropriate paperwork. Gaining residence is difficult to do, so if I were you and you consider that as your highest priority, and just do the best you can on the taxes. Even if you can't maintain tax exempt you should still be able to deduct your time spent in the UAE for work, talk to an aviation tax guy if you need one I could recommend one for you just send me a PM. Good luck.