What is the syntax to sp_recompile logon trigger?
I think I found it:

sp_refreshsqlmodule (Books Online)


  Updates the metadata for the specified non-schema-bound stored procedure, user-defined function, view, DML trigger, database-level DDL trigger, or server-level DDL trigger in the current database.


EXEC sys.sp_refreshsqlmodule
    @name = 'ddl_trig_name',
    @namespace = 'SERVER_DDL_TRIGGER';