Can you go back to the US a month before your green card expires?

Yes provided your stay abroad or outside US was for less than 180 days. If you were outside US for more than a year you would need a reentry permit which you should have filed for using Form I-131 before leaving US. This permit is valid for 2 years and can be used to reenter US if you stayed abroad for more than a year. After you enter US you need to apply asap for green card renewal using Form I-90.