diff --git a/src/or/main.c b/src/or/main.c
index ce510b9bea..1a75158bf4 100644
--- a/src/or/main.c
+++ b/src/or/main.c
@@ -360,6 +360,8 @@ static void run_connection_housekeeping(int i, time_t now) {
         connection_mark_for_close(conn);
         conn->hold_open_until_flushed = 1; /* give it a last chance */
       }
+    } else {
+      connection_mark_for_close(conn);
     }
     return;
   }