diff --git a/store/postgres/src/copy.rs b/store/postgres/src/copy.rs
index e0ae71eab3e..effe2950ee2 100644
--- a/store/postgres/src/copy.rs
+++ b/store/postgres/src/copy.rs
@@ -32,12 +32,13 @@ use diesel::{
 };
 use graph::{
     constraint_violation,
-    futures03::future::select_all,
+    futures03::{future::select_all, FutureExt as _},
     prelude::{
         info, lazy_static, o, warn, BlockNumber, BlockPtr, CheapClone, Logger, StoreError, ENV_VARS,
     },
     schema::EntityType,
     slog::{debug, error},
+    tokio,
 };
 use itertools::Itertools;
 
@@ -687,6 +688,21 @@ impl CopyProgress {
     }
 }
 
+enum WorkerResult {
+    Ok(CopyTableWorker),
+    Err(StoreError),
+    Wake,
+}
+
+impl From<Result<CopyTableWorker, StoreError>> for WorkerResult {
+    fn from(result: Result<CopyTableWorker, StoreError>) -> Self {
+        match result {
+            Ok(worker) => WorkerResult::Ok(worker),
+            Err(e) => WorkerResult::Err(e),
+        }
+    }
+}
+
 /// A helper to run copying of one table. We need to thread `conn` and
 /// `table` from the control loop to the background worker and back again to
 /// the control loop. This worker facilitates that
@@ -705,11 +721,7 @@ impl CopyTableWorker {
         }
     }
 
-    async fn run(
-        mut self,
-        logger: Logger,
-        progress: Arc<CopyProgress>,
-    ) -> Result<Self, StoreError> {
+    async fn run(mut self, logger: Logger, progress: Arc<CopyProgress>) -> WorkerResult {
         let object = self.table.dst.object.cheap_clone();
         graph::spawn_blocking_allow_panic(move || {
             self.result = self.run_inner(logger, &progress);
@@ -717,6 +729,7 @@ impl CopyTableWorker {
         })
         .await
         .map_err(|e| constraint_violation!("copy worker for {} panicked: {}", object, e))
+        .into()
     }
 
     fn run_inner(&mut self, logger: Logger, progress: &CopyProgress) -> Result<Status, StoreError> {
@@ -812,6 +825,57 @@ impl CopyTableWorker {
     }
 }
 
+/// A helper to manage the workers that are copying data. Besides the actual
+/// workers it also keeps a worker that wakes us up periodically to give us
+/// a chance to create more workers if there are database connections
+/// available
+struct Workers {
+    /// The list of workers that are currently running. This will always
+    /// include a future that wakes us up periodically
+    futures: Vec<Pin<Box<dyn Future<Output = WorkerResult>>>>,
+}
+
+impl Workers {
+    fn new() -> Self {
+        Self {
+            futures: vec![Self::waker()],
+        }
+    }
+
+    fn add(&mut self, worker: Pin<Box<dyn Future<Output = WorkerResult>>>) {
+        self.futures.push(worker);
+    }
+
+    fn has_work(&self) -> bool {
+        self.futures.len() > 1
+    }
+
+    async fn select(&mut self) -> WorkerResult {
+        use WorkerResult::*;
+
+        let futures = std::mem::take(&mut self.futures);
+        let (result, _idx, remaining) = select_all(futures).await;
+        self.futures = remaining;
+        match result {
+            Ok(_) | Err(_) => { /* nothing to do */ }
+            Wake => {
+                self.futures.push(Self::waker());
+            }
+        }
+        result
+    }
+
+    fn waker() -> Pin<Box<dyn Future<Output = WorkerResult>>> {
+        let sleep = tokio::time::sleep(ENV_VARS.store.batch_target_duration);
+        Box::pin(sleep.map(|()| WorkerResult::Wake))
+    }
+
+    /// Return the number of workers that are not the waker
+    fn len(&self) -> usize {
+        self.futures.len() - 1
+    }
+}
+
 /// A helper for copying subgraphs
 pub struct Connection {
     /// The connection pool for the shard that will contain the destination
@@ -926,7 +990,7 @@ impl Connection {
         &mut self,
         state: &mut CopyState,
         progress: &Arc<CopyProgress>,
-    ) -> Option<Pin<Box<dyn Future<Output = Result<CopyTableWorker, StoreError>>>>> {
+    ) -> Option<Pin<Box<dyn Future<Output = WorkerResult>>>> {
         let Some(conn) = self.conn.take() else {
             return None;
         };
@@ -947,7 +1011,7 @@ impl Connection {
         &mut self,
         state: &mut CopyState,
         progress: &Arc<CopyProgress>,
-    ) -> Option<Pin<Box<dyn Future<Output = Result<CopyTableWorker, StoreError>>>>> {
+    ) -> Option<Pin<Box<dyn Future<Output = WorkerResult>>>> {
         // It's important that we get the connection before the table since
         // we remove the table from the state and could drop it otherwise
         let Some(conn) = self
@@ -989,19 +1053,15 @@ impl Connection {
 
     /// Wait for all workers to finish. This is called when we a worker has
     /// failed with an error that forces us to abort copying
-    async fn cancel_workers(
-        &mut self,
-        progress: Arc<CopyProgress>,
-        mut workers: Vec<Pin<Box<dyn Future<Output = Result<CopyTableWorker, StoreError>>>>>,
-    ) {
+    async fn cancel_workers(&mut self, progress: Arc<CopyProgress>, mut workers: Workers) {
         progress.cancel();
         error!(
             self.logger,
             "copying encountered an error; waiting for all workers to finish"
         );
-        while !workers.is_empty() {
-            let (result, _, remaining) = select_all(workers).await;
-            workers = remaining;
+        while workers.has_work() {
+            use WorkerResult::*;
+            let result = workers.select().await;
             match result {
                 Ok(worker) => {
                     self.conn = Some(worker.conn);
@@ -1010,6 +1070,7 @@ impl Connection {
                     /* Ignore; we had an error previously */
                     error!(self.logger, "copy worker panicked: {}", e);
                 }
+                Wake => { /* Ignore; this is just a waker */ }
             }
         }
     }
@@ -1031,14 +1092,14 @@ impl Connection {
         //
         // The loop has to be very careful about terminating early so that
         // we do not ever leave the loop with `self.conn == None`
-        let mut workers = Vec::new();
-        while !state.unfinished.is_empty() || !workers.is_empty() {
+        let mut workers = Workers::new();
+        while !state.unfinished.is_empty() || workers.has_work() {
             // We usually add at least one job here, except if we are out of
             // tables to copy. In that case, we go through the `while` loop
             // every time one of the tables we are currently copying
             // finishes
             if let Some(worker) = self.default_worker(&mut state, &progress) {
-                workers.push(worker);
+                workers.add(worker);
             }
             loop {
                 if workers.len() >= self.workers {
@@ -1047,24 +1108,24 @@ impl Connection {
                 let Some(worker) = self.extra_worker(&mut state, &progress) else {
                     break;
                 };
-                workers.push(worker);
+                workers.add(worker);
             }
 
             self.assert_progress(workers.len(), &state)?;
-            let (result, _idx, remaining) = select_all(workers).await;
-            workers = remaining;
+            let result = workers.select().await;
 
             // Analyze `result` and take another trip through the loop if
             // everything is ok; wait for pending workers and return if
             // there was an error or if copying was cancelled.
+            use WorkerResult as W;
             match result {
-                Err(e) => {
+                W::Err(e) => {
                     // This is a panic in the background task. We need to
                     // cancel all other tasks and return the error
                     self.cancel_workers(progress, workers).await;
                     return Err(e);
                 }
-                Ok(worker) => {
+                W::Ok(worker) => {
                     // Put the connection back into self.conn so that we can use it
                     // in the next iteration.
                     self.conn = Some(worker.conn);
@@ -1090,6 +1151,10 @@ impl Connection {
                         }
                     }
                 }
+                W::Wake => {
+                    // nothing to do, just try to create more workers by
+                    // going through the loop again
+                }
             };
         }
         debug_assert!(self.conn.is_some());