diff --git a/changelog.d/5146.bugfix b/changelog.d/5146.bugfix
new file mode 100644
index 000000000..a54abed92
--- /dev/null
+++ b/changelog.d/5146.bugfix
@@ -0,0 +1 @@
+Exclude soft-failed events from forward-extremity candidates: fixes "No forward extremities left!" error.
diff --git a/synapse/handlers/federation.py b/synapse/handlers/federation.py
index 068477888..2202ed699 100644
--- a/synapse/handlers/federation.py
+++ b/synapse/handlers/federation.py
@@ -1916,6 +1916,11 @@ class FederationHandler(BaseHandler):
                     event.room_id, latest_event_ids=extrem_ids,
                 )
 
+            logger.debug(
+                "Doing soft-fail check for %s: state %s",
+                event.event_id, current_state_ids,
+            )
+
             # Now check if event pass auth against said current state
             auth_types = auth_types_for_event(event)
             current_state_ids = [
@@ -1932,7 +1937,7 @@ class FederationHandler(BaseHandler):
                 self.auth.check(room_version, event, auth_events=current_auth_events)
             except AuthError as e:
                 logger.warn(
-                    "Failed current state auth resolution for %r because %s",
+                    "Soft-failing %r because %s",
                     event, e,
                 )
                 event.internal_metadata.soft_failed = True
diff --git a/synapse/storage/events.py b/synapse/storage/events.py
index 881d6d012..2ffc27ff4 100644
--- a/synapse/storage/events.py
+++ b/synapse/storage/events.py
@@ -575,10 +575,11 @@ class EventsStore(
 
         def _get_events(txn, batch):
             sql = """
-            SELECT prev_event_id
+            SELECT prev_event_id, internal_metadata
             FROM event_edges
                 INNER JOIN events USING (event_id)
                 LEFT JOIN rejections USING (event_id)
+                LEFT JOIN event_json USING (event_id)
             WHERE
                 prev_event_id IN (%s)
                 AND NOT events.outlier
@@ -588,7 +589,11 @@ class EventsStore(
             )
 
             txn.execute(sql, batch)
-            results.extend(r[0] for r in txn)
+            results.extend(
+                r[0]
+                for r in txn
+                if not json.loads(r[1]).get("soft_failed")
+            )
 
         for chunk in batch_iter(event_ids, 100):
             yield self.runInteraction("_get_events_which_are_prevs", _get_events, chunk)