Just to let you know, I think my problem is resolved now.
Simply turning off the OneDrive automatic desktop backup/sync seems to have fixed things. After turning off the feature, I replaced my 100+ icons in their proper positions, and after using my PC for several hours yesterday, and after an overnight shutdown and restart this morning, my desktop(s) are still in good order.
I have no idea why OneDrive should mess around with desktop files which it is simply supposed to be copying to the cloud, but then there are very few people outside Microsoft who can understand the company or their software design philosophy!
And I have absolutely no idea how the backup feature came to be turned on. I have a had a Windows 10 update recently, that's the only thing I can think of which could have affected my settings. From now on, whenever I get a Windows update I am going to try to check that none of my settings have been changed without my knowledge.
I will remember the trial version of Fences 6, and may try it out in the future. Unfortunately the full product is outside my budget range right now, and it's disappointing that there doesn't seem to be an upgrade path for loyal previous users.
Thanks for your time and assistance Basj.