diff --git a/app/assets/javascripts/vue_pipelines_index/stage.js.es6 b/app/assets/javascripts/vue_pipelines_index/stage.js.es6
index a9fd1c4b876b583aaa559c7ee1e687f9d011da4a..37688702886c3093ce2003c38cd1284ea99ec98e 100644
--- a/app/assets/javascripts/vue_pipelines_index/stage.js.es6
+++ b/app/assets/javascripts/vue_pipelines_index/stage.js.es6
@@ -40,7 +40,16 @@
           });
       },
       keepGraph(e) {
-        e.stopPropagation();
+        const { target } = e;
+
+        if (~target.className.indexOf('js-ci-action-icon')) return null;
+
+        if (
+          target.parentElement &&
+          ~target.parentElement.className.indexOf('js-ci-action-icon')
+        ) return null;
+
+        return e.stopPropagation();
       },
     },
     computed: {