So can a Labour mayor run for three terms?

Here's an interesting story: BBC News: Mayor expelled from Labour Party. Martin Winter, has been seeking a third term as Mayor of Doncaster "but Labour rules do not allow someone to run for a third time".

So why is he having to go outside the party to pursue this aim, yet Ken Livingstone was put to the people of London yet again? Does Labour believe in term limits or not? Or do the rules change depending on the personality?