I have a solution for that (I get it all the time). Open the Terminal and run 'killall Dock' (without the quotes), and you will see your desktop image appear. It is not practical to run this every time this happens of course. To solve this, open Automator. Select the application template. Then, search for the Run Shell Script command. Drag it into the workflow, and enter in the command 'killall Dock' (again, without the quotes). Save this application to any location you choose. Then open System Preferences, and go to the accounts section. Click on your username, and then on the "Login Items" tab. drag your app that you just created there (but remember to not to delete the app afterwards). Quit System Preferences, and you are all set! If it starts happening again, remove the app from the login items tab.
Linc, based on what you said, I realized that I had made a ton of permission changes from what is default and don't want to have to recreate them.
In the meantime I contacted Apple Support to see if they had any suggestions. They suggested the following - after changing the wall paper in the problem account, restart the system instead of logging out and logging back in. It solved the problem - the wall paper remained changed upon start-up. I don't know if that was the root cause of the problem but it is working now.
I appreciate all your time and advice. Thanks for all your help.