Razwan Ali Anjum was handed a fourth consecutive jail term by a High Court judge in April after he refused to reveal where his daughter was.
Mr Justice Moor imposed a 12-month prison sentence after he found him in contempt of a High Court order instructing him to disclose her whereabouts.
He said Anjum, who is in his late 20s, would not be eligible for release until he had served at least six months.
Judges have previously imposed jail terms of two years, 12 months and another 12 months in the hope that Anjum would provide information.
They have re-jailed Anjum as each sentence neared its end.
More top news
Manchester United manager Louis van Gaal says Ryan Giggs will almost certainly succeed him at Old Trafford.
David Cameron has apologised for experiencing "brain fade" after he forgot which football team he supports.
Fans can finally have their first look at Jared Leto's incarnation of the classic villain in 2016's Suicide Squad