Permanent residents are free to travel outside the United States, and temporary or short-term travel generally does not affect your permanent resident status.
However, if it is determined that you did not intend to make the United States your permanent home, it will be determined that you have renounced your permanent resident status. The general guideline is asking if you have been away from the United States for more than a year.
While short-term trips abroad are generally not problematic, the officer may consider criteria such as intention to visit abroad only temporarily, whether you maintain family and community ties in the US, whether you have work in the US whether you filed US income tax as a resident or otherwise established your intention to return to the United States as your permanent home. Other factors that may be taken into account include whether you have a U.S. postal address, U.S. bank accounts, and a valid U.S. driver’s license, owning real estate or doing business in the U.S., and any other evidence that your absence is temporary.
What if I lose my green card or re-entry permit, or they get stolen or destroyed while I’m temporarily leaving the US?
If you lose your green card or reentry permit, or if it is stolen or destroyed while you are abroad, you may be required to file Form I-131A, Application for Travel Document (Carrier Documentation). This carrier documentation will allow an airline or other transport carrier to board a lawful permanent resident bound for the United States without penalty from the carrier.