diff --git a/bgpd/bgp_network.c b/bgpd/bgp_network.c
index 887caee95e..1394c60b25 100644
--- a/bgpd/bgp_network.c
+++ b/bgpd/bgp_network.c
@@ -438,12 +438,15 @@ static int bgp_accept(struct thread *thread)
 		return -1;
 	}
 
-	/* Check whether max prefix restart timer is set for the peer */
-	if (peer1->t_pmax_restart) {
+	/* Do not try to reconnect if the peer reached maximum
+	 * prefixes, restart timer is still running or the peer
+	 * is shutdown.
+	 */
+	if (BGP_PEER_START_SUPPRESSED(peer1)) {
 		if (bgp_debug_neighbor_events(peer1))
 			zlog_debug(
-				"%s - incoming conn rejected - "
-				"peer max prefix timer is active",
+				"[Event] Incoming BGP connection rejected from %s "
+				"due to maximum-prefix or shutdown",
 				peer1->host);
 		close(bgp_sock);
 		return -1;