diff --git a/src/mux_h2.c b/src/mux_h2.c
index 6b8b7e2..c7b2799 100644
--- a/src/mux_h2.c
+++ b/src/mux_h2.c
@@ -717,7 +717,7 @@
 		} else if (br_data(h2c->mbuf)) {
 			/* pending output data: always the regular data timeout */
 			h2c->task->expire = tick_add_ifset(now_ms, h2c->timeout);
-		} else if (h2c->max_id > 0 && !b_data(&h2c->dbuf)) {
+		} else if (!(h2c->flags & H2_CF_IS_BACK) && h2c->max_id > 0 && !b_data(&h2c->dbuf)) {
 			/* idle after having seen one stream => keep-alive */
 			h2c->task->expire = tick_add_ifset(h2c->idle_start, h2c->proxy->timeout.httpka);
 		} else {