diff --git a/swh/deposit/client.py b/swh/deposit/client.py
--- a/swh/deposit/client.py
+++ b/swh/deposit/client.py
@@ -169,6 +169,9 @@
 
         self.base_url = url.strip("/") + "/"
         self.auth = auth
+        self.session = requests.Session()
+        if auth:
+            self.session.auth = auth
 
     def do(self, method, url, *args, **kwargs):
         """Internal method to deal with requests, possibly with basic http
@@ -181,13 +184,8 @@
             The request's execution
 
         """
-        method_fn = getattr(requests, method)
-
-        if self.auth:
-            kwargs["auth"] = self.auth
-
         full_url = urljoin(self.base_url, url.lstrip("/"))
-        return method_fn(full_url, *args, **kwargs)
+        return self.session.request(method, full_url, *args, **kwargs)
 
 
 class PrivateApiDepositClient(BaseApiDepositClient):
diff --git a/swh/deposit/tests/loader/test_client.py b/swh/deposit/tests/loader/test_client.py
--- a/swh/deposit/tests/loader/test_client.py
+++ b/swh/deposit/tests/loader/test_client.py
@@ -9,6 +9,7 @@
 from urllib.parse import urlparse
 
 import pytest
+from requests import Session
 
 from swh.deposit.client import PrivateApiDepositClient
 from swh.deposit.config import DEPOSIT_STATUS_LOAD_FAILURE, DEPOSIT_STATUS_LOAD_SUCCESS
@@ -208,7 +209,7 @@
     """Update status
 
     """
-    mocked_put = mocker.patch("swh.deposit.client.requests.put")
+    mocked_put = mocker.patch.object(Session, "request")
 
     deposit_client = PrivateApiDepositClient(config=CLIENT_TEST_CONFIG)
     deposit_client.status_update(
@@ -216,6 +217,7 @@
     )
 
     mocked_put.assert_called_once_with(
+        "put",
         "https://nowhere.org/update/status",
         json={
             "status": DEPOSIT_STATUS_LOAD_SUCCESS,
@@ -228,12 +230,13 @@
     """Reading metadata can fail for some reasons
 
     """
-    mocked_put = mocker.patch("swh.deposit.client.requests.put")
+    mocked_put = mocker.patch.object(Session, "request")
 
     deposit_client = PrivateApiDepositClient(config=CLIENT_TEST_CONFIG)
     deposit_client.status_update("/update/status/fail", DEPOSIT_STATUS_LOAD_FAILURE)
 
     mocked_put.assert_called_once_with(
+        "put",
         "https://nowhere.org/update/status/fail",
         json={"status": DEPOSIT_STATUS_LOAD_FAILURE,},
     )