diff --git a/doc/source/whatsnew/v0.24.0.rst b/doc/source/whatsnew/v0.24.0.rst
index 1961ca2febb32..2b8cb81b78c4d 100644
--- a/doc/source/whatsnew/v0.24.0.rst
+++ b/doc/source/whatsnew/v0.24.0.rst
@@ -1321,6 +1321,7 @@ Datetimelike
 - Bug in :class:`DatetimeIndex` and :class:`TimedeltaIndex` where indexing with ``Ellipsis`` would incorrectly lose the index's ``freq`` attribute (:issue:`21282`)
 - Clarified error message produced when passing an incorrect ``freq`` argument to :class:`DatetimeIndex` with ``NaT`` as the first entry in the passed data (:issue:`11587`)
 - Bug in :func:`to_datetime` where ``box`` and ``utc`` arguments were ignored when passing a :class:`DataFrame` or ``dict`` of unit mappings (:issue:`23760`)
+- Bug in :attr:`Series.dt` where the cache would not update properly after an in-place operation (:issue:`24408`)
 - Bug in :class:`PeriodIndex` where comparisons against an array-like object with length 1 failed to raise ``ValueError`` (:issue:`23078`)
 
 Timedelta
diff --git a/pandas/core/indexes/accessors.py b/pandas/core/indexes/accessors.py
index 670c4a2d8a414..791ef8223de98 100644
--- a/pandas/core/indexes/accessors.py
+++ b/pandas/core/indexes/accessors.py
@@ -27,7 +27,6 @@ def __init__(self, data, orig):
         self._parent = data
         self.orig = orig
         self.name = getattr(data, 'name', None)
-        self.index = getattr(data, 'index', None)
         self._freeze()
 
     def _get_values(self):
@@ -71,8 +70,7 @@ def _delegate_property_get(self, name):
             result = take_1d(result, self.orig.cat.codes)
             index = self.orig.index
         else:
-            index = self.index
-
+            index = self._parent.index
         # return the result as a Series, which is by definition a copy
         result = Series(result, index=index, name=self.name)
 
@@ -98,7 +96,7 @@ def _delegate_method(self, name, *args, **kwargs):
         if not is_list_like(result):
             return result
 
-        result = Series(result, index=self.index, name=self.name)
+        result = Series(result, index=self._parent.index, name=self.name)
 
         # setting this object will show a SettingWithCopyWarning/Error
         result._is_copy = ("modifications to a method of a datetimelike "
@@ -261,7 +259,7 @@ def components(self):
         3     0      0        0        3             0             0            0
         4     0      0        0        4             0             0            0
         """  # noqa: E501
-        return self._get_values().components.set_index(self.index)
+        return self._get_values().components.set_index(self._parent.index)
 
     @property
     def freq(self):
diff --git a/pandas/tests/plotting/test_series.py b/pandas/tests/plotting/test_series.py
index b5c69bb9e6443..b857979005f5e 100644
--- a/pandas/tests/plotting/test_series.py
+++ b/pandas/tests/plotting/test_series.py
@@ -890,3 +890,15 @@ def test_misc_bindings(self, mock):
             assert s.plot.lag() == 2
             assert s.plot.autocorrelation() == 2
             assert s.plot.bootstrap() == 2
+
+    @pytest.mark.xfail
+    def test_plot_accessor_updates_on_inplace(self):
+        s = Series([1, 2, 3, 4])
+        _, ax = self.plt.subplots()
+        ax = s.plot(ax=ax)
+        before = ax.xaxis.get_ticklocs()
+
+        s.drop([0, 1], inplace=True)
+        _, ax = self.plt.subplots()
+        after = ax.xaxis.get_ticklocs()
+        tm.assert_numpy_array_equal(before, after)
diff --git a/pandas/tests/series/test_api.py b/pandas/tests/series/test_api.py
index 65f5c59deba36..09e556af883c1 100644
--- a/pandas/tests/series/test_api.py
+++ b/pandas/tests/series/test_api.py
@@ -204,6 +204,11 @@ def test_from_array_deprecated(self):
         with tm.assert_produces_warning(FutureWarning):
             self.series_klass.from_array([1, 2, 3])
 
+    def test_sparse_accessor_updates_on_inplace(self):
+        s = pd.Series([1, 1, 2, 3], dtype="Sparse[int]")
+        s.drop([0, 1], inplace=True)
+        assert s.sparse.density == 1.0
+
 
 class TestSeriesMisc(TestData, SharedWithSparse):
 
@@ -447,6 +452,11 @@ def f(x):
         exp = Series([], dtype='float64', index=Index([], dtype='float64'))
         tm.assert_series_equal(result, exp)
 
+    def test_str_accessor_updates_on_inplace(self):
+        s = pd.Series(list('abc'))
+        s.drop([0], inplace=True)
+        assert len(s.str.lower()) == 2
+
     def test_str_attribute(self):
         # GH9068
         methods = ['strip', 'rstrip', 'lstrip']
@@ -535,6 +545,12 @@ def test_cat_accessor_no_new_attributes(self):
                            match="You cannot add any new attribute"):
             c.cat.xlabel = "a"
 
+    def test_cat_accessor_updates_on_inplace(self):
+        s = Series(list('abc')).astype('category')
+        s.drop(0, inplace=True)
+        s.cat.remove_unused_categories(inplace=True)
+        assert len(s.cat.categories) == 2
+
     def test_categorical_delegations(self):
 
         # invalid accessor
diff --git a/pandas/tests/series/test_datetime_values.py b/pandas/tests/series/test_datetime_values.py
index 745a9eee6c300..895717835c630 100644
--- a/pandas/tests/series/test_datetime_values.py
+++ b/pandas/tests/series/test_datetime_values.py
@@ -485,6 +485,13 @@ def test_dt_accessor_invalid(self, ser):
             ser.dt
         assert not hasattr(ser, 'dt')
 
+    def test_dt_accessor_updates_on_inplace(self):
+        s = Series(pd.date_range('2018-01-01', periods=10))
+        s[2] = None
+        s.fillna(pd.Timestamp('2018-01-01'), inplace=True)
+        result = s.dt.date
+        assert result[0] == result[2]
+
     def test_between(self):
         s = Series(bdate_range('1/1/2000', periods=20).astype(object))
         s[::2] = np.nan