She got her Immigrant Visa in 2004 and came to USA three times - 2004, 2007 and 2010. Her Permanent Resident Card expired in 2014. Is her immigrant visa automatically revoked? How do I know that it has been revoked? Or does she need to revoke it herself? If it is not revoked then how to renew the immigrant visa and Permanent Resident Card?
U.S. immigration law assumes that a person admitted to the United States as an immigrant will live in the United States permanently. Remaining outside the U.S. for more than 12 months may result in the loss of your legal permanent resident status and your green card may be taken away.
U.S. Government personnel (military and direct-hire civil service employees) and their spouses and minor children who hold legal resident status in the United States may remain outside of the United States for the duration of an official overseas assignment, plus four months, without losing their immigrant status. All other immigrants who hold U.S. resident status and reside out of the United States for more than 12 months without prior approval from U.S. Citizenship and Immigration Services (USCIS, formerly INS) must obtain a new immigrant visa to return to the United States. Prior approval from USCIS consists of a re-entry permit which can only be applied for in the United States. The holder of a USCIS re-entry permit may remain outside of the United States up to 24 months. For more details on applying for a re-entry permit please visit the USCIS website.
A former immigrant who has lost U.S. resident status and desires to return to the United States as an immigrant must obtain a new immigrant visa based on either a new, approved immigrant petition or qualify for returning resident status. A U.S. relative (spouse, parent, adult offspring or sibling) or your U.S. employer may file an immigrant petition on your behalf in the normal manner. Information on the various types of immigrant and employment based petitions are contained elsewhere in this website.
We are talking about her green card status here and not her previously expired visa. People who have green cards risk abandonment (losing their green cards) when they are out of usa for more than 6 months. If she was out of this country for that long, I doubt that she will be able to renew it ever again.
When someone gets an immigrant visa, the US government expects the person to live in the U.S. Your mother did not do that.
If your mother wants to live in the U.S., someone (e.g. you if you are a U.S. citizen) will have to sponsor her for another green card.
If your mother just wants to visit in the U.S. from time to time, she should apply for a visitor visa. Judging from the frequency of your mother's visits, a visitor visa might be the better option.
If you do decide to sponsor your mother for another green card, then the best way to ensure she does not get into this situation again, is to encourage her to live in the U.S. for at least 6 months of every year for 5 years after getting her green card. Then she will qualify for U.S. citizenship. After she becomes a U.S. citizen, then she can be outside the U.S. for as long as she wants without compromising her ability to come into the U.S. whenever she wants.