The phrase "damage his status" is correct and usable in written English.
It can be used when discussing the potential negative impact on someone's reputation or standing.
Example: "If he continues to make controversial statements, he may damage his status within the organization."
Alternatives: "harm his reputation" or "undermine his standing."
As for City, they appear to be pinning their hopes on Eliaquim Mangala having a far more productive second season in English football and Vincent Kompany no longer being troubled by the recurring injury issues that have undermined his performances and damaged his status as one of the league's more authoritative players.
André Villas-Boas, the manager in the opposing dugout on Wednesday discovered that his attempt to ease the influence of senior players at Chelsea damaged his own status.
The dismissal is a huge blow to McClaren, who looked to have reinvented himself and gone some way towards repairing the damage to his status following his time as England's manager.
He faces a possible two-year ban from the sport and the loss of his Tour title, as well as damage to his status as one of Spain's top athletes.
An MRI exam showed no structural damage but his status was day to day. - Three coaches were fired in the first quarter of the season.
It goes on to say that the segment caused Moore and his family "severe emotional distress and pain and financial damage, especially given his status as a prominent conservative and a God fearing person of faith".
Members of Voice, which represents 34,752 teachers, lecturers and childcare workers, believe such action could jeopardise the negotiations and damage the status of education workers.
But if the intercept fails, it could damage U.S. status, causing allies to lose faith in American security promises — and perhaps lead to new challenges from rivals.
That did not sit well with President Ma Ying-jeou, who said in a statement that Beijing should not "unilaterally damage the status quo of the hard-fought stability across the Taiwan Strait".
The Scottish Football Association, the FAW and the Irish Football Association all oppose the concept of Team GB, as they fear it could ultimately damage their status as individual countries within Fifa and the voting powers they hold as one of the home nations.
