My prescription eyeglasses added AR-coating,but now,just a month passed,the AR-coating lost and show a little green,I want to know how long can the regular AR-coating last ?

Don`t worry about that,that`s the common case,because AR-coating is green,and its function is to protecting you from radiation.

I suggest you should come back to your optician to have a say, usually it's their responsibility if your coating lost in a short time.