diff --git a/tests/app/conftest.py b/tests/app/conftest.py
index 1f9904612..fa17f3fd3 100644
--- a/tests/app/conftest.py
+++ b/tests/app/conftest.py
@@ -612,7 +612,7 @@ def sample_user_service_permission(sample_user):
     return p_model
 
 
-@pytest.fixture(scope="function")
+@pytest.fixture(scope="session")
 def fake_uuid():
     return "6ce466d0-fd6a-11e5-82f5-e0accb9d11a6"
 
diff --git a/tests/app/template/test_rest.py b/tests/app/template/test_rest.py
index 349230696..0d8205291 100644
--- a/tests/app/template/test_rest.py
+++ b/tests/app/template/test_rest.py
@@ -6,6 +6,8 @@ from datetime import datetime, timedelta
 
 import pytest
 from freezegun import freeze_time
+from hypothesis import given
+from hypothesis import strategies as st
 from sqlalchemy import select
 
 from app import db
@@ -297,6 +299,33 @@ def test_should_be_error_if_service_does_not_exist_on_update(client, fake_uuid):
     assert json_resp["message"] == "No result found"
 
 
+@given(
+    fuzzed_service_id=st.uuids(),
+    fuzzed_template_id=st.uuids(),
+    fuzzed_template_name=st.text(min_size=1, max_size=100),
+)
+def test_fuzz_should_be_error_if_service_does_not_exist_on_update(
+    client, fuzzed_service_id, fuzzed_template_id, fuzzed_template_name
+):
+    """
+    Hypothesis-based fuzz test to ensure that when updating a template
+    for a non-existent service, the API returns a 404 with the correct error message
+    """
+    data = {"name": fuzzed_template_name}
+    data = json.dumps(data)
+    auth_header = create_admin_authorization_header()
+    response = client.post(
+        f"/service/{fuzzed_service_id}/tempalte/{fuzzed_template_id}",
+        headers=[("Content-Type", "application/json"), auth_header],
+        data=data,
+    )
+    json_resp = json.loads(response.get_data(as_text=True))
+
+    assert response.status_code == 404
+    assert json_resp["result"] == "error"
+    assert json_resp["message"] == "No result found"
+
+
 @pytest.mark.parametrize("template_type", [TemplateType.EMAIL])
 def test_must_have_a_subject_on_an_email_template(
     client, sample_user, sample_service, template_type
diff --git a/tests/conftest.py b/tests/conftest.py
index 7ce2c8033..6a596e233 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -38,7 +38,7 @@ def notify_api(notify_app):
     ctx.pop()
 
 
-@pytest.fixture(scope="function")
+@pytest.fixture(scope="session")
 def client(notify_api):
     with notify_api.test_request_context(), notify_api.test_client() as client:
         yield client