I think I have solved it.
As I have said before, it was somewhat random.
I think it is connected to auto pitch correction on one word. Despite all of my testing, the only more or less consistent thing seems to be the presence of the pitch plugin. It is behaving almost like it is being side chained by another track, or is responding to a sub frequency on the vocal track.
Because of the inconsistency, it has been very hard to pin down. One playback in six would be glitch free, then the glitch would move in time and so on.
I still don't understand it. If I played just the short region it was usually fine; if I backed up a few bars it would be there again, even though the pitch plugin only came on for the short region and there was no automation anywhere near the offending part.
Anyway, I've done a destructive pitch correction and after about twenty plays it seems to have gone.
In any case, I'm going to get the singer back!
Thanks for all the help.