diff --git a/server/src/session/transport.rs b/server/src/session/transport.rs
index b075c75..99ca972 100644
--- a/server/src/session/transport.rs
+++ b/server/src/session/transport.rs
@@ -21,12 +21,31 @@
 
 use std::path::{Path, PathBuf};
 use std::process::Stdio;
+use std::sync::LazyLock;
 
 use anyhow::{Context, Result};
 use tokio::process::Child;
+use tokio::sync::Semaphore;
 
 use crate::config::SshConfig;
 
+/// How many [`Transport::capture`] calls may have an ssh connection open at
+/// once, across every setup.
+///
+/// `capture` is what a batch (deleting several imports, listing several
+/// machines) fans out over -- one child `ssh` process per call, all started
+/// within the same tick. Nothing here throttled that, so a batch large
+/// enough to open more connections than the remote sshd's default
+/// `MaxStartups` (10, before it starts randomly refusing) has some of
+/// them come back as "Connection closed" -- not a real failure of the
+/// operation, just too many handshakes landing on the listener at once. Four
+/// keeps a batch comfortably under that ceiling while still overlapping the
+/// network round trips. Long-lived processes (`Transport::spawn`, a
+/// session's own child) don't take a permit: they hold it for the session's
+/// lifetime rather than for one round trip, which would starve every other
+/// probe behind it.
+pub(crate) static CAPTURE_PERMITS: LazyLock<Semaphore> = LazyLock::new(|| Semaphore::new(4));
+
 /// What a driver needs run in order to exist as a process.
 ///
 /// Deliberately just the three things every transport can carry. Anything
diff --git a/server/src/setups.rs b/server/src/setups.rs
index b3d3a82..61d3543 100644
--- a/server/src/setups.rs
+++ b/server/src/setups.rs
@@ -163,6 +163,13 @@ pub fn tidy(value: &str) -> Option<String> {
 /// Runs a launch to completion and returns its stdout.
 impl Transport {
     pub async fn capture(&self, launch: &Launch) -> Result<String> {
+        // See `CAPTURE_PERMITS`: caps how many of these run their ssh
+        // connection at once, so a batch doesn't open more than the remote
+        // sshd tolerates before it starts dropping them.
+        let _permit = super::session::transport::CAPTURE_PERMITS
+            .acquire()
+            .await
+            .expect("capture semaphore is never closed");
         let child = self.spawn(launch, super::session::transport::Streams::Piped)?;
         let output = child
             .wait_with_output()