diff --git a/src/client.rs b/src/client.rs
index cb7e677a..a1a9a781 100644
--- a/src/client.rs
+++ b/src/client.rs
@@ -1468,8 +1468,12 @@ where
     type Output = Result<(), crate::Error>;
 
     fn poll(mut self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Self::Output> {
-        self.inner.maybe_close_connection_if_no_streams();
+        // Snapshot before checking for shutdown: the last reference may be
+        // dropped after the shutdown check, before inner.poll registers a
+        // waker. A snapshot taken after that drop would be false and skip the
+        // self-wake below, leaving the connection pending without closing.
         let had_streams_or_refs = self.inner.has_streams_or_other_references();
+        self.inner.maybe_close_connection_if_no_streams();
         let result = self.inner.poll(cx).map_err(Into::into);
         // if we had streams/refs, and don't anymore, wake up one more time to
         // ensure proper shutdown