diff --git a/swh/web/save_code_now/origin_save.py b/swh/web/save_code_now/origin_save.py
--- a/swh/web/save_code_now/origin_save.py
+++ b/swh/web/save_code_now/origin_save.py
@@ -514,10 +514,11 @@
                 save_request_info = _update_save_request_info(sor, task, task_run)
                 task_status = save_request_info["save_task_status"]
                 # create a new scheduler task only if the previous one has been
-                # already executed
-                if (
-                    task_status == SAVE_TASK_FAILED
-                    or task_status == SAVE_TASK_SUCCEEDED
+                # already or is currently executed
+                if task_status in (
+                    SAVE_TASK_FAILED,
+                    SAVE_TASK_SUCCEEDED,
+                    SAVE_TASK_RUNNING,
                 ):
                     can_create_task = True
                     sor = None
diff --git a/swh/web/save_code_now/tests/test_origin_save_api.py b/swh/web/save_code_now/tests/test_origin_save_api.py
--- a/swh/web/save_code_now/tests/test_origin_save_api.py
+++ b/swh/web/save_code_now/tests/test_origin_save_api.py
@@ -20,6 +20,7 @@
     SAVE_TASK_FAILED,
     SAVE_TASK_NOT_CREATED,
     SAVE_TASK_NOT_YET_SCHEDULED,
+    SAVE_TASK_RUNNING,
     SAVE_TASK_SCHEDULED,
     SAVE_TASK_SUCCEEDED,
     VISIT_STATUS_FAILED,
@@ -277,7 +278,9 @@
     )
 
 
-def test_create_save_request_no_duplicate(api_client, mocker, swh_scheduler):
+def test_create_save_request_no_duplicate_if_already_scheduled(
+    api_client, mocker, swh_scheduler
+):
     origin_url = "https://github.com/webpack/webpack"
 
     check_created_save_request_status(
@@ -317,6 +320,49 @@
     assert len(sors) == 1
 
 
+def test_create_save_request_if_previous_one_is_running(
+    api_client, mocker, swh_scheduler
+):
+    origin_url = "https://github.com/webpack/webpack"
+
+    check_created_save_request_status(
+        api_client,
+        mocker,
+        origin_url,
+        expected_request_status=SAVE_REQUEST_ACCEPTED,
+        expected_task_status=SAVE_TASK_NOT_YET_SCHEDULED,
+    )
+
+    check_save_request_status(
+        api_client,
+        mocker,
+        swh_scheduler,
+        origin_url,
+        expected_request_status=SAVE_REQUEST_ACCEPTED,
+        expected_task_status=SAVE_TASK_RUNNING,
+        scheduler_task_status="next_run_scheduled",
+        scheduler_task_run_status="started",
+    )
+
+    sors = list(
+        SaveOriginRequest.objects.filter(visit_type="git", origin_url=origin_url)
+    )
+    assert len(sors) == 1
+
+    check_created_save_request_status(
+        api_client,
+        mocker,
+        origin_url,
+        expected_request_status=SAVE_REQUEST_ACCEPTED,
+        expected_task_status=SAVE_TASK_NOT_YET_SCHEDULED,
+    )
+
+    sors = list(
+        SaveOriginRequest.objects.filter(visit_type="git", origin_url=origin_url)
+    )
+    assert len(sors) == 2
+
+
 def test_get_save_requests_unknown_origin(api_client, swh_scheduler):
     unknown_origin_url = "https://gitlab.com/foo/bar"
     url = reverse(