Still a bit strange but after checking many files I found that in the three sites (main and 2 sub-domains), in the respective configuration files, I had on the 2 working sites ... var $live_site =' ' and on the other... var $live_site ='www.mydomain.com'.
On the site with the problem is was ... var $live_site ='www.mydomain.com'.
(obviously with the actual domain name)
I did not think therefore that this was any impact on the problem, so I left this until now and I removed the live site address for the problem site and made it ... var $live_site =' ' and hey presto! it is now working perfectly!!
I really don't know why this is as it is working in both ways on the other sites but.... that was the problem resolved.
So I suggest that anyone else who is getting stalling, IN THE BACK END ADMINISTRATION, should try both live site configurations, which is "with" full HTTP address of the website and "without", just leaving the quote marks.
This applies to Joomla 1.5.x only!!!
If they have a problem at the front end then they should read the previous posts in this post to resolve that.
Delighted to have sorted this as it is a great extension.