diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 9a6f6e21e5e..5c179c0bd61 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -47,6 +47,8 @@ Bug fixes
   By `Sebastian Weigand <https://github.com/s-weigand>`_.
 - Fix a regression in the removal of duplicate backend entrypoints (:issue:`5944`, :pull:`5959`)
   By `Kai Mühlbauer <https://github.com/kmuehlbauer>`_.
+- Fix an issue that datasets from being saved when time variables with units that ``cftime`` can parse but pandas can not were present (:pull:`6049`).
+  By `Tim Heap <https://github.com/mx-moth>`_.
 
 Documentation
 ~~~~~~~~~~~~~
diff --git a/xarray/coding/times.py b/xarray/coding/times.py
index ea75219db5a..7d532f8fc38 100644
--- a/xarray/coding/times.py
+++ b/xarray/coding/times.py
@@ -400,8 +400,9 @@ def _cleanup_netcdf_time_units(units):
     delta, ref_date = _unpack_netcdf_time_units(units)
     try:
         units = "{} since {}".format(delta, format_timestamp(ref_date))
-    except OutOfBoundsDatetime:
-        # don't worry about reifying the units if they're out of bounds
+    except (OutOfBoundsDatetime, ValueError):
+        # don't worry about reifying the units if they're out of bounds or
+        # formatted badly
         pass
     return units
 
@@ -482,7 +483,7 @@ def encode_cf_datetime(dates, units=None, calendar=None):
             num = time_deltas / time_delta
         num = num.values.reshape(dates.shape)
 
-    except (OutOfBoundsDatetime, OverflowError):
+    except (OutOfBoundsDatetime, OverflowError, ValueError):
         num = _encode_datetime_with_cftime(dates, units, calendar)
 
     num = cast_to_int_if_safe(num)
diff --git a/xarray/tests/test_coding_times.py b/xarray/tests/test_coding_times.py
index aff2cb8cf3a..930677f75f4 100644
--- a/xarray/tests/test_coding_times.py
+++ b/xarray/tests/test_coding_times.py
@@ -853,6 +853,23 @@ def test_encode_cf_datetime_pandas_min() -> None:
     assert calendar == expected_calendar
 
 
+@requires_cftime
+def test_encode_cf_datetime_invalid_pandas_valid_cftime() -> None:
+    num, units, calendar = encode_cf_datetime(
+        pd.date_range("2000", periods=3),
+        # Pandas fails to parse this unit, but cftime is quite happy with it
+        "days since 1970-01-01 00:00:00 00",
+        "standard",
+    )
+
+    expected_num = [10957, 10958, 10959]
+    expected_units = "days since 1970-01-01 00:00:00 00"
+    expected_calendar = "standard"
+    assert_array_equal(num, expected_num)
+    assert units == expected_units
+    assert calendar == expected_calendar
+
+
 @requires_cftime
 def test_time_units_with_timezone_roundtrip(calendar) -> None:
     # Regression test for GH 2649
diff --git a/xarray/tests/test_formatting.py b/xarray/tests/test_formatting.py
index 9e53cac3aa6..aa4c0c49f81 100644
--- a/xarray/tests/test_formatting.py
+++ b/xarray/tests/test_formatting.py
@@ -188,6 +188,11 @@ def test_pretty_print(self) -> None:
     def test_maybe_truncate(self) -> None:
         assert formatting.maybe_truncate("ß", 10) == "ß"
 
+    def test_format_timestamp_invalid_pandas_format(self) -> None:
+        expected = "2021-12-06 17:00:00 00"
+        with pytest.raises(ValueError):
+            formatting.format_timestamp(expected)
+
     def test_format_timestamp_out_of_bounds(self) -> None:
         from datetime import datetime