diff --git a/homeassistant/components/apcupsd/sensor.py b/homeassistant/components/apcupsd/sensor.py
index 2f8acbc754c..033344cf491 100644
--- a/homeassistant/components/apcupsd/sensor.py
+++ b/homeassistant/components/apcupsd/sensor.py
@@ -540,7 +540,17 @@ class APCUPSdSensor(APCUPSdEntity, SensorEntity):
         data = self.coordinator.data[key]
 
         if self.entity_description.device_class == SensorDeviceClass.TIMESTAMP:
-            self._attr_native_value = dateutil.parser.parse(data)
+            # The date could be "N/A" for certain fields (e.g., XOFFBATT), indicating there is no value yet.
+            if data == "N/A":
+                self._attr_native_value = None
+                return
+
+            try:
+                self._attr_native_value = dateutil.parser.parse(data)
+            except (dateutil.parser.ParserError, OverflowError):
+                # If parsing fails we should mark it as unknown, with a log for further debugging.
+                _LOGGER.warning('Failed to parse date for %s: "%s"', key, data)
+                self._attr_native_value = None
             return
 
         self._attr_native_value, inferred_unit = infer_unit(data)
diff --git a/tests/components/apcupsd/test_sensor.py b/tests/components/apcupsd/test_sensor.py
index 2da69b89531..07ac0c90c04 100644
--- a/tests/components/apcupsd/test_sensor.py
+++ b/tests/components/apcupsd/test_sensor.py
@@ -3,7 +3,6 @@
 from datetime import timedelta
 from unittest.mock import AsyncMock
 
-import dateutil.parser
 import pytest
 from syrupy.assertion import SnapshotAssertion
 
@@ -135,42 +134,64 @@ async def test_manual_update_entity(
     assert state.state == "15.0"
 
 
-@pytest.mark.parametrize("mock_request_status", [MOCK_MINIMAL_STATUS], indirect=True)
+@pytest.mark.parametrize(
+    ("mock_request_status", "entity_id", "known_status"),
+    [
+        pytest.param(
+            # Even though the "LASTSTEST" field is not available, we should still create the entity.
+            MOCK_MINIMAL_STATUS,
+            "sensor.apc_ups_last_self_test",
+            MOCK_MINIMAL_STATUS | {"LASTSTEST": "1970-01-01 00:00:00 +0000"},
+            id="last_self_test_missing",
+        ),
+        pytest.param(
+            MOCK_MINIMAL_STATUS | {"XOFFBATT": "N/A"},
+            "sensor.apc_ups_transfer_from_battery",
+            MOCK_MINIMAL_STATUS | {"XOFFBATT": "1970-01-01 00:00:00 +0000"},
+            id="xoffbatt_na",
+        ),
+        pytest.param(
+            MOCK_MINIMAL_STATUS | {"XOFFBATT": "invalid-time-string"},
+            "sensor.apc_ups_transfer_from_battery",
+            MOCK_MINIMAL_STATUS | {"XOFFBATT": "1970-01-01 00:00:00 +0000"},
+            id="xoffbatt_invalid_time_string",
+        ),
+    ],
+    indirect=["mock_request_status"],
+)
 async def test_sensor_unknown(
     hass: HomeAssistant,
     mock_request_status: AsyncMock,
+    entity_id: str,
+    known_status: dict[str, str],
 ) -> None:
-    """Test if our integration can properly mark certain sensors as unknown when it becomes so."""
-    ups_mode_id = "sensor.apc_ups_mode"
-    last_self_test_id = "sensor.apc_ups_last_self_test"
+    """Test if our integration can properly mark certain sensors as known/unknown when it becomes so."""
+    base_status = mock_request_status.return_value
 
-    assert hass.states.get(ups_mode_id).state == MOCK_MINIMAL_STATUS["UPSMODE"]
-    # Last self test sensor should be added even if our status does not report it initially (it is
-    # a sensor that appears only after a periodical or manual self test is performed).
-    assert hass.states.get(last_self_test_id) is not None
-    assert hass.states.get(last_self_test_id).state == STATE_UNKNOWN
+    # The state should be unknown initially.
+    state = hass.states.get(entity_id)
+    assert state
+    assert state.state == STATE_UNKNOWN
 
-    # Simulate an event (a self test) such that "LASTSTEST" field is being reported, the state of
-    # the sensor should be properly updated with the corresponding value.
-    last_self_test_value = "1970-01-01 00:00:00 +0000"
-    mock_request_status.return_value = MOCK_MINIMAL_STATUS | {
-        "LASTSTEST": last_self_test_value
-    }
+    # Update to a payload that should make the entity known.
+    mock_request_status.return_value = known_status
     future = utcnow() + timedelta(minutes=2)
     async_fire_time_changed(hass, future)
     await hass.async_block_till_done()
-    assert (
-        hass.states.get(last_self_test_id).state
-        == dateutil.parser.parse(last_self_test_value).isoformat()
-    )
 
-    # Simulate another event (e.g., daemon restart) such that "LASTSTEST" is no longer reported.
-    mock_request_status.return_value = MOCK_MINIMAL_STATUS
+    state = hass.states.get(entity_id)
+    assert state
+    assert state.state != STATE_UNKNOWN
+
+    # Revert back to the initial status, and the state should now be unknown again.
+    mock_request_status.return_value = base_status
     future = utcnow() + timedelta(minutes=2)
     async_fire_time_changed(hass, future)
     await hass.async_block_till_done()
-    # The state should become unknown again.
-    assert hass.states.get(last_self_test_id).state == STATE_UNKNOWN
+
+    state = hass.states.get(entity_id)
+    assert state
+    assert state.state == STATE_UNKNOWN
 
 
 @pytest.mark.parametrize(("entity_key", "issue_key"), DEPRECATED_SENSORS.items())