Four top officials are leaving the MPs' expenses watchdog following a spat with Commons Speaker John Bercow.
The independent board members refused to reapply for their posts after Mr Bercow insisted they could not have their terms automatically renewed, as had been expected.
In a tense exchange of letters over the summer, Ipsa chairman Sir Ian Kennedy dismissed the idea that Mr Bercow was legally obliged to hold a full selection process - estimated to cost £100,000.
He also raised concerns over a "perception" that Mr Bercow was seeking to neuter Ipsa by turfing out Sir Scott Baker, Jackie Ballard, Ken Olisa and Isobel Sharp "wholesale" in January.
Sir Ian said: "There is no doubt that Ipsa has taken a number of decisions which have not proved popular with some MPs.
"But in our view, reinforced by the views of others, the decisions have been both necessary and appropriate... I am sure that you would not wish the temporary unpopularity of decisions to be perceived as providing grounds for challenging the continuing membership of those making the decisions."
He added: "It is in nobody's interest for expenses once again to become a live issue in the shape of a debate about the future composition of the Board and what this might say about Ipsa's role as an independent regulator. I make no apologies for pointing out the fact that there is much at stake here, not least the reputation and future standing of Ipsa and indeed the reputation of parliament itself."
In a letter in April, Mr Bercow said the Parliamentary Standards Act 2009 "requires each board position to be subject to fair and open competition at the end of every fixed term".
"I have been advised further that were I, as Speaker, to direct that any appointment be carried out by any procedure other than on merit on the basis of full and open competition, that direction would be amenable to judicial review," he wrote.
But Sir Ian said that only applied to "initial" appointments, and an open competition was only usually held if the serving members' performance had been "unsatisfactory". Highlighting the risk that new board members would be seen as "placemen/women of Parliament", he stressed there was "no good reason" for shaking up the appointments process.