Running the loop continuously

We are on 11.2.0.3. We have a dynamic PL/SQL blocking coming from some other location and while we run that block we get ORA-00001 intermittently. Sometimes the whole block error out with ORA-00001. To fix it we comment the line that returns the error and re-run it. The problem is we have too many PL/SQL blocks to run and its so difficult to edit / comment/ re-run the PL/SQL block again and again.

I've defined the EXCEPTION handler (DUP_VAL_ON_INDEX)  as well but the moment ORA-00001 is encountered the execution stops and it goes into EXCEPTION handler but doesn't error out of PL/SQL block.