diff --git a/doc/chrony.conf.adoc b/doc/chrony.conf.adoc
index be39a27..a187570 100644
--- a/doc/chrony.conf.adoc
+++ b/doc/chrony.conf.adoc
@@ -164,13 +164,12 @@ option can be specified. *chronyd* will not try to poll the server until it is
 enabled to do so (by using the <<chronyc.adoc#online,*online*>> command in
 *chronyc*).
 *auto_offline*:::
-With this option, the server will be assumed to have gone offline when two
-requests have been sent to it without receiving a response. This option avoids
+With this option, the server will be assumed to have gone offline when sending
+a request fails, e.g. due to a missing route to the network. This option avoids
 the need to run the <<chronyc.adoc#offline,*offline*>> command from *chronyc*
-when disconnecting the network link, if it is safe to assume that the requests
-and responses will not be dropped in the network, e.g. in a trusted local
-network. (It will still be necessary to use the <<chronyc.adoc#online,*online*>>
-command when the link has been established, to enable measurements to start.)
+when disconnecting the network link. (It will still be necessary to use the
+<<chronyc.adoc#online,*online*>> command when the link has been established, to
+enable measurements to start.)
 *prefer*:::
 Prefer this source over sources without the *prefer* option.
 *noselect*:::
diff --git a/ntp_core.c b/ntp_core.c
index c9d0969..991e3d9 100644
--- a/ntp_core.c
+++ b/ntp_core.c
@@ -89,8 +89,8 @@ struct NCR_Instance_Record {
   int tx_suspended;             /* Boolean indicating we can't transmit yet */
 
   int auto_burst;               /* If 1, initiate a burst on each poll */
-  int auto_offline;             /* If 1, automatically go offline if server/peer
-                                   isn't responding */
+  int auto_offline;             /* If 1, automatically go offline when requests
+                                   cannot be sent */
 
   int local_poll;               /* Log2 of polling interval at our end */
   int remote_poll;              /* Log2 of server/peer's polling interval (recovered
@@ -1143,10 +1143,6 @@ transmit_timeout(void *arg)
       break;
   }
 
-  /* With auto_offline take the source offline on 2nd missed reply */
-  if (inst->auto_offline && inst->tx_count >= 2)
-    NCR_SetConnectivity(inst, SRC_OFFLINE);
-
   if (inst->opmode == MD_OFFLINE) {
     return;
   }
@@ -1230,6 +1226,10 @@ transmit_timeout(void *arg)
     SRC_UpdateReachability(inst->source, 0);
   }
 
+  /* With auto_offline take the source offline if sending failed */
+  if (!sent && inst->auto_offline)
+    NCR_SetConnectivity(inst, SRC_OFFLINE);
+
   switch (inst->opmode) {
     case MD_BURST_WAS_ONLINE:
       /* When not reachable, don't stop online burst until sending succeeds */
@@ -1239,6 +1239,8 @@ transmit_timeout(void *arg)
     case MD_BURST_WAS_OFFLINE:
       --inst->burst_total_samples_to_go;
       break;
+    case MD_OFFLINE:
+      return;
     default:
       break;
   }