diff --git a/scrapy/core/engine.py b/scrapy/core/engine.py
index 6602f661d..1228e78da 100644
--- a/scrapy/core/engine.py
+++ b/scrapy/core/engine.py
@@ -257,9 +257,7 @@ class ExecutionEngine:
 
     def download(self, request: Request, spider: Optional[Spider] = None) -> Deferred:
         """Return a Deferred which fires with a Response as result, only downloader middlewares are applied"""
-        if spider is None:
-            spider = self.spider
-        else:
+        if spider is not None:
             warnings.warn(
                 "Passing a 'spider' argument to ExecutionEngine.download is deprecated",
                 category=ScrapyDeprecationWarning,
@@ -267,7 +265,7 @@ class ExecutionEngine:
             )
             if spider is not self.spider:
                 logger.warning("The spider '%s' does not match the open spider", spider.name)
-        if spider is None:
+        if self.spider is None:
             raise RuntimeError(f"No open spider to crawl: {request}")
         return self._download(request, spider).addBoth(self._downloaded, request, spider)
 
@@ -278,11 +276,14 @@ class ExecutionEngine:
         self.slot.remove_request(request)
         return self.download(result, spider) if isinstance(result, Request) else result
 
-    def _download(self, request: Request, spider: Spider) -> Deferred:
+    def _download(self, request: Request, spider: Optional[Spider]) -> Deferred:
         assert self.slot is not None  # typing
 
         self.slot.add_request(request)
 
+        if spider is None:
+            spider = self.spider
+
         def _on_success(result: Union[Response, Request]) -> Union[Response, Request]:
             if not isinstance(result, (Response, Request)):
                 raise TypeError(f"Incorrect type: expected Response or Request, got {type(result)}: {result!r}")
diff --git a/scrapy/downloadermiddlewares/httpproxy.py b/scrapy/downloadermiddlewares/httpproxy.py
index 1deda42bd..dd8a7e797 100644
--- a/scrapy/downloadermiddlewares/httpproxy.py
+++ b/scrapy/downloadermiddlewares/httpproxy.py
@@ -78,4 +78,7 @@ class HttpProxyMiddleware:
                     del request.headers[b'Proxy-Authorization']
                 del request.meta['_auth_proxy']
         elif b'Proxy-Authorization' in request.headers:
-            del request.headers[b'Proxy-Authorization']
+            if proxy_url:
+                request.meta['_auth_proxy'] = proxy_url
+            else:
+                del request.headers[b'Proxy-Authorization']

diff --git a/tests/test_downloadermiddleware_httpproxy.py b/tests/test_downloadermiddleware_httpproxy.py
index 70eb94d77..44434f90e 100644
--- a/tests/test_downloadermiddleware_httpproxy.py
+++ b/tests/test_downloadermiddleware_httpproxy.py
@@ -400,6 +400,9 @@ class TestHttpProxyMiddleware(TestCase):
         self.assertNotIn(b'Proxy-Authorization', request.headers)
 
     def test_proxy_authentication_header_proxy_without_credentials(self):
+        """As long as the proxy URL in request metadata remains the same, the
+        Proxy-Authorization header is used and kept, and may even be
+        changed."""
         middleware = HttpProxyMiddleware()
         request = Request(
             'https://example.com',
@@ -408,7 +411,16 @@ class TestHttpProxyMiddleware(TestCase):
         )
         assert middleware.process_request(request, spider) is None
         self.assertEqual(request.meta['proxy'], 'https://example.com')
-        self.assertNotIn(b'Proxy-Authorization', request.headers)
+        self.assertEqual(request.headers['Proxy-Authorization'], b'Basic foo')
+
+        assert middleware.process_request(request, spider) is None
+        self.assertEqual(request.meta['proxy'], 'https://example.com')
+        self.assertEqual(request.headers['Proxy-Authorization'], b'Basic foo')
+
+        request.headers['Proxy-Authorization'] = b'Basic bar'
+        assert middleware.process_request(request, spider) is None
+        self.assertEqual(request.meta['proxy'], 'https://example.com')
+        self.assertEqual(request.headers['Proxy-Authorization'], b'Basic bar')
 
     def test_proxy_authentication_header_proxy_with_same_credentials(self):
         middleware = HttpProxyMiddleware()

Scrapy warns about itself
I'm using Scrapy 2.6.2. Created a new project, run a spider, and there is 

```
2022-08-02 23:50:26 [py.warnings] WARNING: [redacted]/python3.8/site-packages/scrapy/core/engine.py:279: ScrapyDeprecationWarning: Passing a 'spider' argument to ExecutionEngine.download is deprecated
  return self.download(result, spider) if isinstance(result, Request) else result
```

message in logs. We also have the same warning in our testing suite, but I haven't realized it's not a test-only issue.
tests/test_downloadermiddleware_httpproxy.py::TestHttpProxyMiddleware::test_proxy_authentication_header_proxy_without_credentials
tests/test_downloadermiddleware_httpproxy.py::TestHttpProxyMiddleware::test_add_credentials tests/test_downloadermiddleware_httpproxy.py::TestHttpProxyMiddleware::test_add_proxy_with_credentials tests/test_downloadermiddleware_httpproxy.py::TestHttpProxyMiddleware::test_add_proxy_without_credentials tests/test_downloadermiddleware_httpproxy.py::TestHttpProxyMiddleware::test_change_credentials tests/test_downloadermiddleware_httpproxy.py::TestHttpProxyMiddleware::test_change_proxy_add_credentials tests/test_downloadermiddleware_httpproxy.py::TestHttpProxyMiddleware::test_change_proxy_change_credentials tests/test_downloadermiddleware_httpproxy.py::TestHttpProxyMiddleware::test_change_proxy_keep_credentials tests/test_downloadermiddleware_httpproxy.py::TestHttpProxyMiddleware::test_change_proxy_remove_credentials tests/test_downloadermiddleware_httpproxy.py::TestHttpProxyMiddleware::test_change_proxy_remove_credentials_preremoved_header tests/test_downloadermiddleware_httpproxy.py::TestHttpProxyMiddleware::test_environment_proxies tests/test_downloadermiddleware_httpproxy.py::TestHttpProxyMiddleware::test_no_environment_proxies tests/test_downloadermiddleware_httpproxy.py::TestHttpProxyMiddleware::test_no_proxy tests/test_downloadermiddleware_httpproxy.py::TestHttpProxyMiddleware::test_no_proxy_invalid_values tests/test_downloadermiddleware_httpproxy.py::TestHttpProxyMiddleware::test_not_enabled tests/test_downloadermiddleware_httpproxy.py::TestHttpProxyMiddleware::test_proxy_already_seted tests/test_downloadermiddleware_httpproxy.py::TestHttpProxyMiddleware::test_proxy_auth tests/test_downloadermiddleware_httpproxy.py::TestHttpProxyMiddleware::test_proxy_auth_empty_passwd tests/test_downloadermiddleware_httpproxy.py::TestHttpProxyMiddleware::test_proxy_auth_encoding tests/test_downloadermiddleware_httpproxy.py::TestHttpProxyMiddleware::test_proxy_authentication_header_disabled_proxy tests/test_downloadermiddleware_httpproxy.py::TestHttpProxyMiddleware::test_proxy_authentication_header_proxy_with_different_credentials tests/test_downloadermiddleware_httpproxy.py::TestHttpProxyMiddleware::test_proxy_authentication_header_proxy_with_same_credentials tests/test_downloadermiddleware_httpproxy.py::TestHttpProxyMiddleware::test_proxy_authentication_header_undefined_proxy tests/test_downloadermiddleware_httpproxy.py::TestHttpProxyMiddleware::test_proxy_precedence_meta tests/test_downloadermiddleware_httpproxy.py::TestHttpProxyMiddleware::test_remove_credentials tests/test_downloadermiddleware_httpproxy.py::TestHttpProxyMiddleware::test_remove_proxy_with_credentials tests/test_downloadermiddleware_httpproxy.py::TestHttpProxyMiddleware::test_remove_proxy_without_credentials