I don't think you need worry about. My mom stayed here 6 years(92-98), only first 1.5 years she had valid b2 status. She went travel with us many times by flight with her valid chinese passport. She even came to visit us again in 2002 and 2006. During 2002, I took my parent to Europe from US and they got another 6 months visa extension at the US customs when they came back from 14 days trip. Same in 2006, they got visa extension again when they came back from mexican cruise.