Apparently it is possible for the value of "Auto arrange icons" be out of step with the displayed value in the "View" options of the list from right-clicking blank desktop space. If this happens, Windows 7 may persist in auto arranging each time it starts
despite the fact that Auto Arrange does not appear to be selected.
A solution that worked for me is to:
SET the Auto Arrange option;
Do a restart that way;
Then uncheck the Auto Arrange option;
And do another restart.
This seemed to get the Auto Arrange function behavior back in sync with the displayed value of the option, and stopped Windows 7 from auto arranging on startup.
This problem may have come about through use or mis-use of "DesktopOK" mentioned in other replies.