Mr Brennan, 77, has been missing from his home in Wheeldon Avenue, Derby, since 4.45pm on Monday 17th December 2012.
Police have widened their search to Worksop and Welbeck, as he has friends in this area of Notts.
Mr Brennan’s daughter Cindy Beadling-Brennan said Christmas had been a very difficult time for all the family.
“This is so out of character for him. He is such a family man. We are trying to stay strong as best we can but we just want to know where he is and want him to come home,” she said.
The family has also released a new, more recent, image of him.
Officers are becoming increasingly concerned for Mr Brennan’s safety as he has memory loss.
The weather has also been poor and he is without his medication.
Mr Brennan is a keen dog walker and police are asking people to remain vigilant, particularly if they are out walking, and look out for anyone fitting his description.
He is described as white, 5ft 7in tall, of slim build, with brown short hair that is going grey.
He was last seen wearing brown denim trousers with a red cross on the back pocket, a brown cotton type jacket with a wool lining and a fur collar.
He could be wearing a cap. And he walks with a stoop.
Anyone who sees Mr Brennan should call Derbyshire Police on 101.