It is difficult to predict what US immigration officials will do when your parents return to the USA. US officials at ports of entry have broad authority to admit or deny entry, and to set the length of time for authorized stay. It is possible that your parents could receive another 6 months, but it is also possible that the authorized time could be less.
If your parents have interest in becoming permanent residents of the USA, perhaps there is a family member, an adult son or daughter (perhaps you?) who is a US Citizen who could help your parents to obtain permanent resident status.
You should consult with an immigration attorney about the situation.
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Possibly, but it is also possible that they would be denied entry.
You should retain an experienced immigration lawyer to review all the facts, advise you, and handle the case. You can find one through http://www.ailalawyer.com.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.
You are proposing that you parents engaged in what is called the "revolving door" by departing and attempting to quickly re-enter the United States. This can be fraught with problems if it is clear that they are simply trying to extend their stay. The better alternative in this case is to apply for an extension of the authorized stay without leaving the U.S.
Your parents should consult with an experienced immigration attorney who can review the facts of their case, advise them of the options available, and how best to proceed.
While this answer is provided by a Florida Bar Certified Expert in Immigration and Nationality Law, it is for general information purposes only and an attorney/client relationship is neither intended nor created. You should seek out qualified counsel to review your case and provide you with advice specific to your situation. Call +1-561-478-5353 to schedule a consultation with Mr. Devore.