diff --git a/lib/Backend/SftpReadStream.php b/lib/Backend/SftpReadStream.php
index 99ee417..1c9ff13 100644
--- a/lib/Backend/SftpReadStream.php
+++ b/lib/Backend/SftpReadStream.php
@@ -55,6 +55,13 @@ final class SftpReadStream {
 	 */
 	private static ?\WeakMap $chunks = null;
 	private static int $requestId = 0x4e470000;
+	/**
+	 * Connections whose server did not confirm closing a batch's files: readMany() is not used on
+	 * them again, so handles cannot pile up.
+	 *
+	 * @var \WeakMap<object, true>|null
+	 */
+	private static ?\WeakMap $noBatches = null;
 	/** Streams in a row that failed; at MAX_FAILURES only the storage's own stream is used. */
 	private static int $failures = 0;
 	public const MAX_FAILURES = 3;
@@ -182,7 +189,7 @@ final class SftpReadStream {
 			self::$failures++;
 			return null;
 		}
-		if ($sftp === null) {
+		if ($sftp === null || self::$noBatches?->offsetExists($sftp) === true) {
 			return null;
 		}
 		$result = array_fill_keys($paths, null);
@@ -200,8 +207,9 @@ final class SftpReadStream {
 				$result[$path] = $contents;
 			}
 			if (!$closed) {
-				// The server did not confirm closing these files: no more batches, so handles
-				// cannot pile up. The rest is read the usual way, one at a time.
+				// The server did not confirm closing these files: no more batches on this
+				// connection, so handles cannot pile up. The rest is read the usual way.
+				self::noMoreBatches($sftp);
 				break;
 			}
 		}
@@ -209,6 +217,11 @@ final class SftpReadStream {
 		return $result;
 	}
 
+	private static function noMoreBatches(object $sftp): void {
+		self::$noBatches ??= new \WeakMap();
+		self::$noBatches[$sftp] = true;
+	}
+
 	private static function disconnect(object $sftp): void {
 		try {
 			if (is_callable([$sftp, 'disconnect'])) {
@@ -306,6 +319,7 @@ final class SftpReadStream {
 	/** Test hook: forget the learned READ sizes and earlier failures. */
 	public static function reset(): void {
 		self::$chunks = null;
+		self::$noBatches = null;
 		self::$failures = 0;
 	}
 
diff --git a/tests/Unit/Backend/SftpReadStreamTest.php b/tests/Unit/Backend/SftpReadStreamTest.php
index 2542b53..bff6a4b 100644
--- a/tests/Unit/Backend/SftpReadStreamTest.php
+++ b/tests/Unit/Backend/SftpReadStreamTest.php
@@ -286,6 +286,8 @@ class SftpReadStreamTest extends TestCase {
 		$this->assertSame('file 31', $got['31']);
 		$this->assertNull($got['32'], 'no second batch after unconfirmed closes');
 		$this->assertCount(SftpReadStream::BATCH, array_filter($got, fn ($v) => $v !== null));
+		// Nor on a later call over the same connection.
+		$this->assertNull(SftpReadStream::readMany(new FakeSftpStorage($sftp), ['0']));
 	}
 
 	public function testReadManyLeavesAMalformedAnswerToTheCaller(): void {