This is a bad bad issue created by 4.3. Like many others I was going mad with tracking this down. I’d recently moved servers on one of my sites and I thought that might be the issue.
Many thanks to those that contributed to the fix, it worked fine and I am grateful.
But why isn’t there a generic 4.3.1 fix released yet? I have over a hundred sites on a variety of hosts and manually checking which are blasting the poor hosts to death and fixing them is not something I relish.