If I work for an airline outside of US can I stay for longer than six months ( as in not moving to the US completely ) provided I commute often , at times more than once a month. I just got my green card and want to stay working abroad for a bit longer so I can save up. Thank you.

You may be able to travel and stay outside of the US for up to one year at a time. However, it is not recommended as you need to be in the US for at least 6 months a year otherwise it jeopardizes your naturalization application.

By the way, you have to file your tax return, and don't claim your status as "non-resident even you stay outside US for over 183 days.