The post which Penny Thompson is leaving next week after less than three years has become the impossible job.

Chief executives of the city council in Brighton and Hove depart with alarming regularity at great cost to the people who pay them.

They barely have time to slip their feet under the table at King’s House, the headquarters, before they are on their way.

David Panter, brilliant and alternative, unexpectedly left to pursue a much more minor career down under.

Alan McCarthy, the local boy made good, departed after a spat with the Tory leadership at the time.

John Barradell failed to live up to his promise and there were few tears shed when he went.

Now Penny Thompson is going in a hurry and it’s clear the new Labour administration felt it could not get on with her.

These chief executives are in charge of the biggest employer in the city with a multi-million pound budget. They are among the top public officials in the country.

They have impeccable credentials.

Yet the average length of stay is only just over three years before they quit.

The cost in farewell payments is more than a million pounds and there are further large sums to be paid in recruiting them.

Why don’t they last longer? The answer is that the council is not now controlled by a single political party.

For most of its life there have been minority administrations – Labour, Tory, Green and now Labour once again.

Chief executives have to spend inordinate amounts of time dealing with the politicians to see what is possible and what is not.

To say the least it is a tricky task and their reward is often to receive the obloquy of at last one party.

It was not always like that.

Glynn Jones, chief executive when the city council was formed, enjoyed a long and fruitful period in office,

He formed close ties with Lord Bassam and his Labour colleagues who had a working majority in the council chamber in an era generally considered to have been successful for Brighton and Hove.

The Tory opposition was suspicious of Mr Jones when he arrived as he had previously worked for the left-wing council in Haringey, London.

But with courtesy and charm he won them over, demonstrating all the while that he was the servant of whichever party happened to be in control of the council at the time.

Going further back to an era when Brighton and Hove had separate councils, long service was the order of the day.

Wily old Reg Morgan, the first Brighton chief executive, served for more than a decade while Bill Dodd, the last town clerk, held the top job for 20 years.

Councillors were often in awe of this official who seemed to know everything and had been around forever. He was even nicknamed Almighty Dodd.

But there was no question of either him or Reg Morgan leaving Brighton before their well-deserved retirements.

Penny Thompson has plenty to be proud of during her short tenure at the top.

She was particularly good at bringing disparate groups of people together and seeing what progress could be made with them working together.

Hacking through the officialise of her farewell statement, it is possible to glean that she is leaving the council in far better shape than it was when she took over.

But her departure is disruptive for the authority and a bad start for the new Labour leadership. You’d think it would want to keep a top official who had plenty more skill and energy to give to the city.

Whoever takes her place will have arrived in the knowledge that no recent predecessor has managed to stay in a council bedevilled by petty party politics.

It really makes me wonder if local democracy is the best way of running an authority vital to the lives of everyone in the city.

We pay more than a million pounds a year on councillors’ allowances only to see some of them fight each other and make the city ungovernable.

Penny Thompson will disappear with her golden handshake even though she would far rather have carried on working. There will be warm words of welcome for her successor but the chances of a happy ending must be slight.