I have needed to move on from Windows Live Mail, for the reasons stated by Trouble.
Bot, the problem is not connected with the lack of sync, it is a random occurrence and, I would put it down as an unsolved bug.
The first operation for deleting them has been successful, but the computer/mail program has not recorded it. The easiest way I found, was to drag and drop them into the deleted folder. It will be , possibly, only one of the mails which is causing the problem, so you may find, if you have a number of them, that you will hit on the baddy and from then it iwill begin to operate normally again.
You can, if you wish, hold the shift key and select the messages one by one, until you get a popup saying a particular one cannot be selected.