SYMPTOM:
Users are able to delete some logical tables that are used by objects but not all tables. Some tables get the message below preventing them from being deleted while others get the warning but upon selecting yes are removed. The first image below shows the warning message box that will be displayed at any time a table is deleted. The next image is the error that shows for certain tables that the product does not allow to be removed after selecting yes in the warning.
warning:

error:

Cannot delete 'LU_Gender' because other objects depend on it. Do you want to search the dependent objects?

ACTION:
If it is desired to prevent users from being able to delete any logical tables period, the easiest option is to use ACL's to make sure users/groups do not have the delete access to those objects. This can be done at the tables folder so it will apply to all newly created logical tables as well.