“I’m originally from Ireland.  In 2004 my husband and I moved to New York after winning visas via the green card lottery.  We stayed for about a year and a half and decided to move back home in 2005 when I became pregnant. 
“In May of last year we took our daughter on a trip to New York. We had accepted the fact that our green cards were no longer valid as we were out of the country over 12 months, so we completed holiday visas.  When we went through immigration they informed us that our visas were still okay but that our daughter was not legal. But because she was under two years old and this was our first trip back to New York, she could be stamped automatically and given a green card.  
“Cut a long story short, she was given a stamp on her passport which is valid for 12 months and is up in May 2008.  We were delighted as we were not expecting this and our minds went into overdrive thinking about how we could move back to New York with a child.
“I am writing because her actual green card has not arrived at the address we use in New York.  I know that it took a few months for our green cards to arrive but hers green card seems to be very late.  Do you think there could be a problem with it?  Is there anyone I could call? 
“When we met with immigration I told them that we would be moving back to New York in a few months, but we plan to move back in April of 2008.  I'm hoping this will be okay that we will have no problems because we are inside the 12 month time period. 
“Maybe I'm being paranoid, but do you think that they have placed a note on her file saying not to issue the card unless requested because they didn't believe that we were going to move back for sure?  I don't want to have any issues or problems because we will be giving up our jobs and home to move back, and it would be devastating if we didn't get in legally.”
You're not going to have problems, and it’s actually good to hear stories of U.S. Customs and Border Patrol officers being kind to the public it serves!
It’s not surprising that, back in May of 2007, you thought your green cards would be of no use because of your lengthy absence from the U.S. Physical presence in the country is a standard requirement that permanent residents must adhere to, with any absences of a year or more generally termed as an abandonment of residence (and, therefore, status, unless the absence is authorized via a re-entry permit or a returning resident visa.)
However, there are exceptions where the physical presence requirement can be overlooked, even if the green card holder has not obtained the aforementioned permit/visa. One of those instances is when the resident is pregnant and gives birth abroad.
The officer you encountered last May therefore correctly informed you that your green cards were still valid for re-entry and subsequent use in the U.S. Of course your case was helped by the fact that your absence from the U.S. didn’t last for years and years, but rather a period of approximately two years. 
The officer was also correct in stating that your child, because you were returning to the U.S. with her before her second birthday, would automatically be admitted as a permanent resident. 
Her physical green card, however, was likely not mailed to the address you provided – or else it was rejected by the U.S. postal system – if it is an address that doesn’t usually receive your mail. This is what often happens with government-issued mail – it has to be sent to an addressee’s usual address, or else it will get returned to sender. Certainly, you can be assured that nothing sinister happened with your child’s green card.
To find out more, phone the U.S. Citizenship and Immigration Service customer service center at 1-800-375-5283. If the card is lost in the system, which it may well be, you can apply for a new one using an I-90 form. Visit for more information.