diff --git a/Cargo.lock b/Cargo.lock
index a7f74567ea2..a284eb8cce3 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -3039,7 +3039,7 @@ dependencies = [
 
 [[package]]
 name = "libp2p-swarm"
-version = "0.43.4"
+version = "0.43.5"
 dependencies = [
  "async-std",
  "either",
diff --git a/Cargo.toml b/Cargo.toml
index be26badcc30..4932efb58ee 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -100,7 +100,7 @@ libp2p-rendezvous = { version = "0.13.0", path = "protocols/rendezvous" }
 libp2p-upnp = { version = "0.1.1", path = "protocols/upnp" }
 libp2p-request-response = { version = "0.25.1", path = "protocols/request-response" }
 libp2p-server = { version = "0.12.3", path = "misc/server" }
-libp2p-swarm = { version = "0.43.4", path = "swarm" }
+libp2p-swarm = { version = "0.43.5", path = "swarm" }
 libp2p-swarm-derive = { version = "0.33.0", path = "swarm-derive" }
 libp2p-swarm-test = { version = "0.2.0", path = "swarm-test" }
 libp2p-tcp = { version = "0.40.0", path = "transports/tcp" }
diff --git a/swarm/CHANGELOG.md b/swarm/CHANGELOG.md
index 2d5fcfe542d..230134862df 100644
--- a/swarm/CHANGELOG.md
+++ b/swarm/CHANGELOG.md
@@ -1,3 +1,8 @@
+## 0.43.5
+
+- Fix overflow in `KeepAlive` computation that could occur if `SwarmBuilder::idle_connection_timeout` is configured with `u64::MAX`.
+  See [PR 4559](https://github.com/libp2p/rust-libp2p/pull/4559).
+
 ## 0.43.4
 
 - Implement `Debug` for event structs.
diff --git a/swarm/Cargo.toml b/swarm/Cargo.toml
index c2de4cb624a..a991bacd53e 100644
--- a/swarm/Cargo.toml
+++ b/swarm/Cargo.toml
@@ -3,7 +3,7 @@ name = "libp2p-swarm"
 edition = "2021"
 rust-version = { workspace = true }
 description = "The libp2p swarm"
-version = "0.43.4"
+version = "0.43.5"
 authors = ["Parity Technologies <admin@parity.io>"]
 license = "MIT"
 repository = "https://github.com/libp2p/rust-libp2p"
diff --git a/swarm/src/connection.rs b/swarm/src/connection.rs
index 310cf3a81e3..d99319cf2cb 100644
--- a/swarm/src/connection.rs
+++ b/swarm/src/connection.rs
@@ -361,15 +361,16 @@ where
                     }
                 }
                 (_, KeepAlive::Until(earliest_shutdown)) => {
-                    if let Some(requested_keep_alive) =
-                        earliest_shutdown.checked_duration_since(Instant::now())
-                    {
-                        let effective_keep_alive = max(requested_keep_alive, *idle_timeout);
+                    let now = Instant::now();
+
+                    if let Some(requested) = earliest_shutdown.checked_duration_since(now) {
+                        let effective_keep_alive = max(requested, *idle_timeout);
+
+                        let safe_keep_alive = checked_add_fraction(now, effective_keep_alive);
 
                         // Important: We store the _original_ `Instant` given by the `ConnectionHandler` in the `Later` instance to ensure we can compare it in the above branch.
                         // This is quite subtle but will hopefully become simpler soon once `KeepAlive::Until` is fully deprecated. See <https://github.com/libp2p/rust-libp2p/issues/3844>/
-                        *shutdown =
-                            Shutdown::Later(Delay::new(effective_keep_alive), earliest_shutdown)
+                        *shutdown = Shutdown::Later(Delay::new(safe_keep_alive), earliest_shutdown)
                     }
                 }
                 (_, KeepAlive::No) if idle_timeout == &Duration::ZERO => {
@@ -379,8 +380,10 @@ where
                     // Do nothing, i.e. let the shutdown timer continue to tick.
                 }
                 (_, KeepAlive::No) => {
-                    let deadline = Instant::now() + *idle_timeout;
-                    *shutdown = Shutdown::Later(Delay::new(*idle_timeout), deadline);
+                    let now = Instant::now();
+                    let safe_keep_alive = checked_add_fraction(now, *idle_timeout);
+
+                    *shutdown = Shutdown::Later(Delay::new(safe_keep_alive), now + safe_keep_alive);
                 }
                 (_, KeepAlive::Yes) => *shutdown = Shutdown::None,
             };
@@ -479,6 +482,20 @@ fn gather_supported_protocols(handler: &impl ConnectionHandler) -> HashSet<Strea
         .collect()
 }
 
+/// Repeatedly halves and adds the [`Duration`] to the [`Instant`] until [`Instant::checked_add`] succeeds.
+///
+/// [`Instant`] depends on the underlying platform and has a limit of which points in time it can represent.
+/// The [`Duration`] computed by the this function may not be the longest possible that we can add to `now` but it will work.
+fn checked_add_fraction(start: Instant, mut duration: Duration) -> Duration {
+    while start.checked_add(duration).is_none() {
+        log::debug!("{start:?} + {duration:?} cannot be presented, halving duration");
+
+        duration /= 2;
+    }
+
+    duration
+}
+
 /// Borrowed information about an incoming connection currently being negotiated.
 #[derive(Debug, Copy, Clone)]
 pub(crate) struct IncomingInfo<'a> {
@@ -957,6 +974,16 @@ mod tests {
         ));
     }
 
+    #[test]
+    fn checked_add_fraction_can_add_u64_max() {
+        let _ = env_logger::try_init();
+        let start = Instant::now();
+
+        let duration = checked_add_fraction(start, Duration::from_secs(u64::MAX));
+
+        assert!(start.checked_add(duration).is_some())
+    }
+
     struct KeepAliveUntilConnectionHandler {
         until: Instant,
     }