The most likely reason for this would be that the System Folder is protected. Look at the control panel, General Controls, and see if "Protect System Folder" is checked. If so, un-check it, move the Trash icon to where you want it and restart. After the computer has restarted, you may re-select "Protect System Folder" and the Trash icon will stay where you have placed it.
This article was published in the 18 June 1997 "Information Alley".