Hey there,
I have just had some luck with this issue, after learning to live with it for the past few months, after doing something atrocious to my permissions.
Here's what I did.
1. Followed instructions to show all files (including hidden files) from
http://osxdaily.com/2009/02/25/show-hidden-files-in-os-x/ (don't forget to relaunch Finder!)
2. go to the your desktop folder, and delete the .DS_Store file that is now visible. This file stores all the meta data for the icons on your desktop, including its size and location.
*note: if you can't delete the file due to insufficient permissions, right click the file, select Get Info, and at the bottom of the window, there is "Sharing and Permissions". You will need to change the "privelege" for your user to "Read and Write"
3. To test, I moved a few icons from where they keep getting rearranged to
3. At this point, I have re-hidden the hidden files using the instructions from the website above.
4. Relaunch Finder, and the icons that were moved in step 3 SHOULD stay in their location
5. You're done!
I hope that this helps.
Cheers,