Yes, you may remain in the United States. Your visa is simply an entry document. Your authorized stay in the United States is controlled by your I-94 and I-20. You will need to apply for a new visa when you need to travel outside the United States. You can read more about student visas at http://myattorneyusa.com/student-visas.
Answered on Aug 22nd, 2016 at 12:53 PM