diff --git a/src/mux_h2.c b/src/mux_h2.c
index 626739c..ebefd52 100644
--- a/src/mux_h2.c
+++ b/src/mux_h2.c
@@ -2297,7 +2297,7 @@
 	}
 
 	if (h2c->task) {
-		if (eb_is_empty(&h2c->streams_by_id)) {
+		if (eb_is_empty(&h2c->streams_by_id) || h2c->mbuf->o) {
 			h2c->task->expire = tick_add(now_ms, h2c->last_sid < 0 ? h2c->timeout : h2c->shut_timeout);
 			task_queue(h2c->task);
 		}
@@ -2468,7 +2468,7 @@
 			h2_release(h2c->conn);
 		}
 		else if (h2c->task) {
-			if (eb_is_empty(&h2c->streams_by_id)) {
+			if (eb_is_empty(&h2c->streams_by_id) || h2c->mbuf->o) {
 				h2c->task->expire = tick_add(now_ms, h2c->last_sid < 0 ? h2c->timeout : h2c->shut_timeout);
 				task_queue(h2c->task);
 			}