diff --git a/src/mux_h2.c b/src/mux_h2.c
index 47df89e38..5fc754721 100644
--- a/src/mux_h2.c
+++ b/src/mux_h2.c
@@ -2493,6 +2493,7 @@ static void h2_detach(struct conn_stream *cs)
 	 */
 	if (eb_is_empty(&h2c->streams_by_id) &&     /* don't close if streams exist */
 	    ((h2c->conn->flags & CO_FL_ERROR) ||    /* errors close immediately */
+	     (h2c->st0 >= H2_CS_ERROR && !h2c->task) || /* a timeout stroke earlier */
 	     (h2c->flags & H2_CF_GOAWAY_FAILED) ||
 	     (!h2c->mbuf->o &&  /* mux buffer empty, also process clean events below */
 	      (conn_xprt_read0_pending(h2c->conn) ||