diff --git a/scripts/ci/brotli-safe-composer.sh b/scripts/ci/brotli-safe-composer.sh
index 7fb4c3c8b..ab6836be6 100755
--- a/scripts/ci/brotli-safe-composer.sh
+++ b/scripts/ci/brotli-safe-composer.sh
@@ -38,9 +38,21 @@ if test "${1:-}" = --check; then
 fi
 
 if ! docker image inspect "$image" > /dev/null 2>&1; then
-    printf 'FROM %s\nLABEL dw.composer.base="%s"\nRUN apk add --no-cache --upgrade "%s" && apk info -e "%s"\n' \
+    # Fetching Alpine's package index fails now and then on CI runners; the
+    # build is retried twice before the failure is reported.
+    attempt=1
+    until printf 'FROM %s\nLABEL dw.composer.base="%s"\nRUN apk add --no-cache --upgrade "%s" && apk info -e "%s"\n' \
         "$base" "$base" "$floor" "$floor" \
         | docker build --quiet --tag "$image" - > /dev/null
+    do
+        if test "$attempt" -ge 3; then
+            echo "Building $image failed $attempt times" >&2
+            exit 1
+        fi
+        echo "Building $image failed (attempt $attempt); retrying" >&2
+        sleep $((attempt * 10))
+        attempt=$((attempt + 1))
+    done
 fi
 # The derived image must still be the pinned one plus the fixed decoder.
 parent=$(docker image inspect --format '{{index .Config.Labels "dw.composer.base"}}' "$image")
diff --git a/scripts/conformance/server-parity/schedule-probe.php b/scripts/conformance/server-parity/schedule-probe.php
index 1f10e3b91..fa8e9e38d 100644
--- a/scripts/conformance/server-parity/schedule-probe.php
+++ b/scripts/conformance/server-parity/schedule-probe.php
@@ -63,7 +63,9 @@ function prepareHttpSchedule(Client $client, array $fixture, string $scheduleId,
     } else {
         // The separate installed schedule:evaluate role fires the original
         // occurrence. This probe never moves a deadline or writes target rows.
-        $deadline = microtime(true) + 10;
+        // Each pass of that role boots the application twice, which can take
+        // several seconds on a loaded CI runner.
+        $deadline = microtime(true) + 25;
         do {
             $history = parityScheduleHistory($client, $scheduleId);
             $trigger = parityScheduleTrigger($history);
@@ -73,7 +75,7 @@ function prepareHttpSchedule(Client $client, array $fixture, string $scheduleId,
                 break;
             }
             if (microtime(true) >= $deadline) {
-                throw new RuntimeException('The installed scheduler did not fire the original occurrence within ten seconds.');
+                throw new RuntimeException('The installed scheduler did not fire the original occurrence within 25 seconds.');
             }
             usleep(50000);
         } while (true);
diff --git a/tests/Unit/Support/composer_trust_test.py b/tests/Unit/Support/composer_trust_test.py
index a52353639..5a97ba8bb 100644
--- a/tests/Unit/Support/composer_trust_test.py
+++ b/tests/Unit/Support/composer_trust_test.py
@@ -421,6 +421,46 @@ def test_other_failures_commands_and_kept_containers_are_not_retried(self) -> No
                 result, runs = self.retrying(1, failure, *arguments)
                 self.assertEqual((100, 1), (result.returncode, runs), result.stderr)
 
+    def building(self, failures: int) -> tuple[subprocess.CompletedProcess[str], int]:
+        """Runs a copy of the floor script whose image build fails `failures` times."""
+        work = Path(tempfile.mkdtemp(prefix="dw-brotli-floor-retry-"))
+        self.addCleanup(shutil.rmtree, work, ignore_errors=True)
+        (work / "bin").mkdir()
+        shutil.copy(FLOOR_SCRIPT, work / "brotli-safe-composer.sh")
+        base = re.search(r"^base=(\S+)$", FLOOR_SCRIPT.read_text(), re.MULTILINE).group(1)
+        count = work / "builds"
+        docker = work / "bin" / "docker"
+        docker.write_text(f"""#!/bin/sh
+case "$1 $2" in
+  "image inspect")
+    if [ "$3" = --format ]; then echo '{base}'; exit 0; fi
+    exit 1 ;;
+  "build --quiet")
+    cat > /dev/null
+    n=$(($(cat '{count}' 2>/dev/null || echo 0) + 1)); echo "$n" > '{count}'
+    if [ "$n" -le {failures} ]; then echo 'ERROR: unable to fetch the package index' >&2; exit 5; fi
+    exit 0 ;;
+  "run --rm") exit 0 ;;
+esac
+exit 64
+""")
+        (work / "bin" / "sleep").write_text("#!/bin/sh\nexit 0\n")
+        for stub in (docker, work / "bin" / "sleep"):
+            stub.chmod(0o755)
+        result = subprocess.run(["sh", str(work / "brotli-safe-composer.sh")], capture_output=True, text=True,
+                                env={**os.environ, "PATH": f"{work / 'bin'}:{os.environ['PATH']}"}, timeout=60)
+        return result, int(count.read_text())
+
+    def test_the_floor_build_retries_a_transient_failure_twice(self) -> None:
+        result, builds = self.building(2)
+        self.assertEqual((0, 3), (result.returncode, builds), result.stderr)
+        self.assertEqual("dw-composer-brotli-floor:2.10.3-da624c2c705d\n", result.stdout)
+        self.assertEqual(2, result.stderr.count("retrying"), result.stderr)
+
+        result, builds = self.building(3)
+        self.assertEqual((1, 3), (result.returncode, builds), "three attempts at most")
+        self.assertIn("failed 3 times", result.stderr)
+
     def test_the_floor_refuses_the_pinned_image_and_accepts_its_own(self) -> None:
         docker_or_skip(self)
         refused = subprocess.run(["sh", str(FLOOR_SCRIPT), "--check", PINNED_COMPOSER],