In OSX 10.9.5 my desktop folders re-arrange when a new window is opened. I have "sort by" off. I can arrange my folders and then when I open a new window (not every time) all of the folders will randomly rearrange to avoid the new window. What gives?
Usually this is a corrupt .DS_Store file. Delete it and see if your shaky folder clears up.
In finder - press command + shift + .
Then you can delete the file and revert the setting to show hidden files if you wish to not see them.