Sometimes, you just can't delete a feature class from ArcCatalog. Maybe something got messed up in the database, or the feature class was incorrectly created. For whatever reason, ArcCatalog won't allow you to delete the feature class.
This is probably not the right way, but it's how I have had to do it (in Oracle):
set serveroutput on;
DECLARE
v_tbl varchar(50) := 'RPT_REGION'; -- SET THIS TABLE
v_schema varchar(50);
BEGIN
select sys_context('userenv','current_schema') into v_schema from dual;
DBMS_OUTPUT.PUT_LINE(v_schema || '.' || v_tbl);
DBMS_OUTPUT.PUT_LINE('DELETING FROM table_registry');
DELETE FROM table_registry WHERE table_name = v_tbl;
DBMS_OUTPUT.PUT_LINE('DELETING FROM column_registry');
DELETE FROM column_registry WHERE table_name = v_tbl;
DBMS_OUTPUT.PUT_LINE('DELETING FROM layers');
DELETE FROM layers WHERE table_name = v_tbl;
DBMS_OUTPUT.PUT_LINE('DELETING FROM geometry_columns');
DELETE FROM geometry_columns WHERE f_table_name = v_tbl;
DBMS_OUTPUT.PUT_LINE('DELETING FROM gdb_items');
DELETE FROM gdb_items WHERE physicalname = v_schema || '.' || v_tbl;
commit;
END;
Then Drop your table, and you can re-import it.
Branch of Re: ArcGIS Server 10.3 Question about deleting SDE feature class