After using the delete key to delete an object in the schema browser on the left hand side, if I try to delete another object, the delete key does not work. It will not delete the object.
For some reason, if the object that becomes highlighted right after another object is deleted stays highlighted, then the delete key does not work. Click on another object, so that the object that became highlighted after deleting the previous object becomes un-highlighted, then you can use the delete key to delete any of the objects again.
Waiting for fix to be released in a future version of Toad for Oracle.