Don't close sudoers_fp, keep it open and set close on exec flag instead.

parse.c

@@ -125,10 +125,6 @@ sudoers_lookup(pwflag)
     set_perms(PERM_RUNAS);
     error = yyparse();
 
-    /* Close the sudoers file now that we are done with it. */
-    (void) fclose(sudoers_fp);
-    sudoers_fp = NULL;
-
     if (error || parse_error) {
 	set_perms(PERM_ROOT);
 	return(VALIDATE_ERROR);

sudo.c

@@ -915,6 +915,7 @@ check_sudoers()
 	if (sudoers_fp == NULL)
 	    log_error(USE_ERRNO, "can't open %s", _PATH_SUDOERS);
     }
+    (void) fcntl(fileno(sudoers_fp), F_SETFD, 1);
 
     set_perms(PERM_ROOT);		/* change back to root */
 }