How to timeout with SSE (server sent events)

[Gumichocopengin8]

Summary

I use SSE and the SSE sends data infinitely in my app. I wanna set timeout but not sure how to do it against SSE.
Anyone has any ideas?

I tried this to timeout after 3 sec, but didn't work as expected.

 Router::new()
        .nest("/api", api)
        .layer(
            ServiceBuilder::new()
                .layer(HandleErrorLayer::new(|err: BoxError| async move {
                    (
                        StatusCode::INTERNAL_SERVER_ERROR,
                        format!("Unhandled error: {}", err),
                    )
                }))
                .layer(TimeoutLayer::new(Duration::from_secs(3))),
        )

axum version

0.8.1