diff --git a/patroni/api.py b/patroni/api.py
index 657744fd..47f4ce9b 100644
--- a/patroni/api.py
+++ b/patroni/api.py
@@ -845,7 +845,10 @@ class RestApiServer(ThreadingMixIn, HTTPServer, Thread):
 
     def shutdown_request(self, request):
         if hasattr(request, 'context'):  # SSLSocket
-            request.unwrap()
+            try:
+                request.unwrap()
+            except Exception as e:
+                logger.debug('Failed to shutdown SSL connection: %r', e)
         super(RestApiServer, self).shutdown_request(request)
 
     def get_certificate_serial_number(self):
diff --git a/tests/test_api.py b/tests/test_api.py
index a1db15f3..37228980 100644
--- a/tests/test_api.py
+++ b/tests/test_api.py
@@ -601,8 +601,11 @@ class TestRestApiServer(unittest.TestCase):
         self.srv.process_request_thread(Mock(), '2')
 
     @patch.object(MockRestApiServer, 'process_request', Mock(side_effect=RuntimeError))
-    @patch.object(MockRestApiServer, 'get_request', Mock(return_value=(Mock(), ('127.0.0.1', 55555))))
-    def test_process_request_error(self):
+    @patch.object(MockRestApiServer, 'get_request')
+    def test_process_request_error(self, mock_get_request):
+        mock_request = Mock()
+        mock_request.unwrap.side_effect = Exception
+        mock_get_request.return_value = (mock_request, ('127.0.0.1', 55555))
         self.srv._handle_request_noblock()
 
     @patch('ssl._ssl._test_decode_cert', Mock())