diff --git a/Lib/logging/handlers.py b/Lib/logging/handlers.py
index e225a21da408fad..9d31cd4bc3a1018 100644
--- a/Lib/logging/handlers.py
+++ b/Lib/logging/handlers.py
@@ -469,6 +469,7 @@ def doRollover(self):
                 timeTuple = time.localtime(t + addend)
         dfn = self.rotation_filename(self.baseFilename + "." +
                                      time.strftime(self.suffix, timeTuple))
+        self.rolloverAt = self.computeRollover(currentTime)
         if os.path.exists(dfn):
             # Already rolled over.
             return
@@ -482,7 +483,6 @@ def doRollover(self):
                 os.remove(s)
         if not self.delay:
             self.stream = self._open()
-        self.rolloverAt = self.computeRollover(currentTime)
 
 class WatchedFileHandler(logging.FileHandler):
     """
diff --git a/Lib/test/test_logging.py b/Lib/test/test_logging.py
index b1852ee43b594fa..d94a79b3c5dd155 100644
--- a/Lib/test/test_logging.py
+++ b/Lib/test/test_logging.py
@@ -6902,6 +6902,32 @@ def test_rollover_at_midnight(self, weekly=False):
     def test_rollover_at_weekday(self):
         self.test_rollover_at_midnight(weekly=True)
 
+    def test_rollover_backup_exists(self):
+        fh = logging.handlers.TimedRotatingFileHandler(
+            self.fn, 'S', encoding="utf-8", delay=True, utc=True)
+        self.addCleanup(fh.close)
+        rolloverAt = fh.rolloverAt
+        dfn = self.fn + time.strftime(".%Y-%m-%d_%H-%M-%S",
+                                      time.gmtime(rolloverAt - 1))
+        os_helper.create_empty_file(dfn)
+        self.rmfiles.append(dfn)
+        with patch('time.time', return_value=rolloverAt):
+            fh.doRollover()
+        self.assertEqual(fh.rolloverAt, rolloverAt + 1)
+
+    def test_rollover_error(self):
+        fh = logging.handlers.TimedRotatingFileHandler(
+            self.fn, 'S', encoding="utf-8", utc=True)
+        self.addCleanup(fh.close)
+        rolloverAt = fh.rolloverAt
+        dfn = self.fn + time.strftime(".%Y-%m-%d_%H-%M-%S",
+                                      time.gmtime(rolloverAt - 1))
+        self.rmfiles.append(dfn)
+        with (patch('time.time', return_value=rolloverAt),
+              patch.object(fh, '_open', side_effect=OSError)):
+            self.assertRaises(OSError, fh.doRollover)
+        self.assertEqual(fh.rolloverAt, rolloverAt + 1)
+
     def test_invalid(self):
         assertRaises = self.assertRaises
         assertRaises(ValueError, logging.handlers.TimedRotatingFileHandler,
diff --git a/Misc/NEWS.d/next/Library/2026-10-19-02-38-17.gh-issue-159690.d1hW68.rst b/Misc/NEWS.d/next/Library/2026-10-19-02-38-17.gh-issue-159690.d1hW68.rst
new file mode 100644
index 000000000000000..8da1aaf178a50f0
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2026-10-19-02-38-17.gh-issue-159690.d1hW68.rst
@@ -0,0 +1,2 @@
+Fix :class:`logging.handlers.TimedRotatingFileHandler` so that it no longer
+stops rolling over when a rollover fails or its backup file already exists.