diff --git a/zebra-network/src/peer/client.rs b/zebra-network/src/peer/client.rs
index 8def31c22..f5e4e2ea2 100644
--- a/zebra-network/src/peer/client.rs
+++ b/zebra-network/src/peer/client.rs
@@ -12,7 +12,7 @@ use tower::Service;
 
 use crate::protocol::internal::{Request, Response};
 
-use super::{ErrorSlot, SharedPeerError};
+use super::{ErrorSlot, PeerError, SharedPeerError};
 
 /// The "client" duplex half of a peer connection.
 pub struct Client {
@@ -148,6 +148,8 @@ impl Service<Request> for Client {
         }) {
             Err(e) => {
                 if e.is_disconnected() {
+                    let ClientRequest { tx, .. } = e.into_inner();
+                    let _ = tx.send(Err(PeerError::ConnectionClosed.into()));
                     future::ready(Err(self
                         .error_slot
                         .try_get_error()
diff --git a/zebra-network/src/peer/handshake.rs b/zebra-network/src/peer/handshake.rs
index 5bdfcd03f..af7ec7fd3 100644
--- a/zebra-network/src/peer/handshake.rs
+++ b/zebra-network/src/peer/handshake.rs
@@ -30,7 +30,7 @@ use crate::{
     BoxError, Config,
 };
 
-use super::{Client, Connection, ErrorSlot, HandshakeError};
+use super::{Client, Connection, ErrorSlot, HandshakeError, PeerError};
 
 /// A [`Service`] that handshakes with a remote peer and constructs a
 /// client/server pair.
@@ -464,19 +464,39 @@ where
                                 let (tx, rx) = oneshot::channel();
                                 let request = Request::Ping(Nonce::default());
                                 tracing::trace!(?request, "queueing heartbeat request");
-                                if server_tx
-                                    .send(ClientRequest {
-                                        request,
-                                        tx: tx.into(),
-                                        span: tracing::Span::current(),
-                                    })
-                                    .await
-                                    .is_err()
-                                {
-                                    tracing::trace!(
-                                        "error sending heartbeat request, shutting down"
-                                    );
-                                    return;
+                                match server_tx.try_send(ClientRequest {
+                                    request,
+                                    tx: tx.into(),
+                                    span: tracing::Span::current(),
+                                }) {
+                                    Ok(()) => {
+                                        match server_tx.flush().await {
+                                            Ok(()) => {}
+                                            Err(e) => {
+                                                // TODO: we can't get the client request for this failure,
+                                                // so we can't ensure the invariant holds
+                                                panic!("flushing client request failed: {:?}", e);
+                                            }
+                                        }
+                                    }
+                                    Err(e) => {
+                                        tracing::trace!(
+                                            ?e,
+                                            "error sending heartbeat request, shutting down"
+                                        );
+                                        if e.is_disconnected() {
+                                            let ClientRequest { tx, .. } = e.into_inner();
+                                            let _ =
+                                                tx.send(Err(PeerError::ConnectionClosed.into()));
+                                        } else if e.is_full() {
+                                            let ClientRequest { tx, .. } = e.into_inner();
+                                            let _ = tx.send(Err(PeerError::Overloaded.into()));
+                                        } else {
+                                            // we need to map unexpected error types to PeerErrors
+                                            panic!("unexpected try_send error: {:?}", e);
+                                        }
+                                        return;
+                                    }
                                 }
                                 // Heartbeats are checked internally to the
                                 // connection logic, but we need to wait on the