diff --git a/pyproject.toml b/pyproject.toml
index 9755776..0361928 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -38,6 +38,13 @@ pydocvi = "pydocvi.cli:main"
 
 [dependency-groups]
 dev = [
+    # Not used by the package, and here because it is what Sphinx reads these
+    # files with. polib is more forgiving than Babel, so a test that reads our
+    # own output back with our own reader agrees with itself and proves nothing:
+    # it passed the whole time the corpus was shipping a PO-Revision-Date that
+    # made Sphinx skip every catalog. The consumer's parser is the only one whose
+    # opinion decides whether the site has any Vietnamese on it.
+    "babel>=2.16",
     "pytest>=8.3",
     "pytest-cov>=6",
     "pytest-asyncio>=0.25",
diff --git a/src/pydocvi/apply.py b/src/pydocvi/apply.py
index c95eaee..815af63 100644
--- a/src/pydocvi/apply.py
+++ b/src/pydocvi/apply.py
@@ -19,6 +19,7 @@
 
 from collections.abc import Iterable, Sequence
 from dataclasses import dataclass
+from datetime import UTC, datetime
 from pathlib import Path
 
 from pydocvi import __version__, catalog, classify
@@ -67,6 +68,44 @@
 PASSTHROUGH_FIELD = "passthrough="
 
 
+#: How this tool stamps a run, everywhere a run is named: in the queue, in the
+#: ``run=`` field of a provenance comment, and in the memory.
+RUN_DATE = "%Y-%m-%dT%H:%MZ"
+
+#: How the PO header is defined to write a date, which is not ISO 8601 and is
+#: the whole reason :func:`po_date` exists.
+PO_DATE = "%Y-%m-%d %H:%M%z"
+
+
+def po_date(when: str) -> str:
+    """A run stamp in the format ``PO-Revision-Date`` is defined to use.
+
+    The two are not the same and the difference is not cosmetic. A run is
+    stamped ``2026-08-18T03:55Z`` because that is what a run is called
+    everywhere else in this tool, and the PO header wants ``2026-08-18
+    03:55+0000``. Babel's reader raises on the ``T`` and the ``Z``, Sphinx
+    catches that as a reading error and skips writing the ``.mo`` for that
+    catalog, and every page in it then renders in English.
+
+    Nothing anywhere reports this. Not Sphinx, which logs a warning among
+    thousands and carries on; not the build, which succeeds; not the coverage
+    table, which counts the .po files and is entirely right about them. The
+    published site simply loses every translation it has. That is what happened
+    to all 548 catalogs and all 1 437 reviewed strings on the first deploy after
+    ``apply`` started writing headers, and the only way anybody found out was
+    reading the rendered HTML.
+
+    A date already in the right shape is handed back untouched, so a date
+    written by Transifex survives a round trip through ``apply`` unchanged and
+    only the ones this tool got wrong are rewritten.
+    """
+    try:
+        parsed = datetime.strptime(when, RUN_DATE).replace(tzinfo=UTC)
+    except ValueError:
+        return when
+    return parsed.strftime(PO_DATE)
+
+
 class ApplyError(ValueError):
     """The catalogs and the memory disagree in a way writing cannot resolve."""
 
@@ -93,7 +132,7 @@ class Stamp:
     @property
     def revised(self) -> str:
         """The header's ``PO-Revision-Date``, which defaults to the run."""
-        return self.revision or self.run
+        return po_date(self.revision or self.run)
 
 
 @dataclass(frozen=True, slots=True, kw_only=True)
diff --git a/tests/test_apply.py b/tests/test_apply.py
index 89d2f6c..680e787 100644
--- a/tests/test_apply.py
+++ b/tests/test_apply.py
@@ -308,9 +308,38 @@ def test_it_says_the_translations_are_machine_made_and_unreviewed(self) -> None:
         assert out.metadata["Last-Translator"] == "pydocvi (machine translation, unreviewed)"
 
     def test_the_project_and_the_date_come_from_the_stamp(self) -> None:
+        """The date is the run, rewritten into the format the PO header is
+        defined to use. This asserted the run verbatim until August 2026, which
+        is how a corpus shipped with an ISO date in a field that is not ISO."""
         out = applied(upstream(block("Dealing with Bugs")), Memory())
         assert out.metadata["Project-Id-Version"] == "Python 3.15"
-        assert out.metadata["PO-Revision-Date"] == "2026-08-17T09:30Z"
+        assert out.metadata["PO-Revision-Date"] == "2026-08-17 09:30+0000"
+
+    def test_a_date_already_in_the_right_shape_is_left_alone(self) -> None:
+        """So a date written by Transifex survives a round trip through apply,
+        and only the ones this tool got wrong are rewritten."""
+        stamp = Stamp(
+            project="Python 3.15", run="2026-08-17T09:30Z", revision="2025-09-16 00:00+0000"
+        )
+        out = apply.header(upstream(block("Dealing with Bugs")), stamp)
+        assert out.metadata["PO-Revision-Date"] == "2025-09-16 00:00+0000"
+
+    def test_sphinx_can_read_the_file_back(self) -> None:
+        """The one that matters, and it has to use Babel rather than polib.
+
+        polib reads our ISO date without complaint, so every test we had agreed
+        with itself while Sphinx was refusing the whole catalog. Babel is what
+        Sphinx reads with: it raises on the date, Sphinx logs one warning among
+        thousands and skips writing the .mo, the build succeeds, and the
+        published page comes out in English. 548 catalogs and 1 437 reviewed
+        strings went out that way.
+        """
+        from io import StringIO
+
+        from babel.messages.pofile import read_po
+
+        out = applied(upstream(block("Dealing with Bugs")), Memory())
+        assert read_po(StringIO(catalog.render(out)), locale="vi").revision_date is not None
 
     def test_vietnamese_gets_one_plural_form(self) -> None:
         out = applied(upstream(block("Dealing with Bugs")), Memory())
diff --git a/uv.lock b/uv.lock
index c7727bc..22fdb74 100644
--- a/uv.lock
+++ b/uv.lock
@@ -100,6 +100,15 @@ wheels = [
     { url = "https://files.pythonhosted.org/packages/25/6c/b400476d3ceba681ab929787edc9554f6d88fcc69435eb681b00fc0457a5/ast_serialize-0.8.0-cp39-abi3-win_arm64.whl", hash = "sha256:b2a5978662fd4db463dfb4b974d2b10ac6430b98f5333aabc7051909df3561d0", size = 1083655, upload-time = "2026-08-07T11:29:00.349Z" },
 ]
 
+[[package]]
+name = "babel"
+version = "2.18.0"
+source = { registry = "https://pypi.org/simple" }
+sdist = { url = "https://files.pythonhosted.org/packages/7d/b2/51899539b6ceeeb420d40ed3cd4b7a40519404f9baf3d4ac99dc413a834b/babel-2.18.0.tar.gz", hash = "sha256:b80b99a14bd085fcacfa15c9165f651fbb3406e66cc603abf11c5750937c992d", size = 9959554, upload-time = "2026-02-01T12:30:56.078Z" }
+wheels = [
+    { url = "https://files.pythonhosted.org/packages/77/f5/21d2de20e8b8b0408f0681956ca2c69f1320a3848ac50e6e7f39c6159675/babel-2.18.0-py3-none-any.whl", hash = "sha256:e2b422b277c2b9a9630c1d7903c2a00d0830c409c59ac8cae9081c92f1aeba35", size = 10196845, upload-time = "2026-02-01T12:30:53.445Z" },
+]
+
 [[package]]
 name = "certifi"
 version = "2026.7.22"
@@ -669,7 +678,7 @@ wheels = [
 
 [[package]]
 name = "python-docs-vi-translator"
-version = "0.1.0"
+version = "0.1.2"
 source = { editable = "." }
 dependencies = [
     { name = "httpx" },
@@ -683,6 +692,7 @@ dependencies = [
 
 [package.dev-dependencies]
 dev = [
+    { name = "babel" },
     { name = "hypothesis" },
     { name = "mypy" },
     { name = "pre-commit" },
@@ -705,6 +715,7 @@ requires-dist = [
 
 [package.metadata.requires-dev]
 dev = [
+    { name = "babel", specifier = ">=2.16" },
     { name = "hypothesis", specifier = ">=6.120" },
     { name = "mypy", specifier = ">=1.14" },
     { name = "pre-commit", specifier = ">=4" },