diff --git a/kopf/_core/engines/probing.py b/kopf/_core/engines/probing.py
index 0c1bbb99..fb7e7ece 100644
--- a/kopf/_core/engines/probing.py
+++ b/kopf/_core/engines/probing.py
@@ -79,10 +79,10 @@ async def get_health(
     app = aiohttp.web.Application()
     app.add_routes([aiohttp.web.get(path, get_health)])
 
-    runner = aiohttp.web.AppRunner(app, handle_signals=False)
+    runner = aiohttp.web.AppRunner(app, handle_signals=False, shutdown_timeout=1.0)
     await runner.setup()
 
-    site = aiohttp.web.TCPSite(runner, host, port, shutdown_timeout=1.0)
+    site = aiohttp.web.TCPSite(runner, host, port)
     await site.start()
 
     # Log with the actual URL: normalised, with hostname/port set.
diff --git a/requirements.txt b/requirements.txt
index 65a2a83c..619d8e32 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -17,7 +17,7 @@ pre-commit
 pyngrok
 pytest>=6.0.0
 pytest-aiohttp
-pytest-asyncio
+pytest-asyncio<0.22  # until the "event_loop" deprecation is solved
 pytest-cov
 pytest-mock
 pytest-timeout
diff --git a/tests/test_liveness.py b/tests/test_liveness.py
index 35cc578f..47cc8ead 100644
--- a/tests/test_liveness.py
+++ b/tests/test_liveness.py
@@ -34,8 +34,10 @@ async def liveness_url(settings, liveness_registry, unused_tcp_port_factory):
         )
     )
 
+    # Generally there is no or minimal timeout, except if the runner/server raise on start up.
+    # In that case, escalate their error from the task instead of hanging here forever.
     try:
-        await ready_flag.wait()
+        await asyncio.wait_for(ready_flag.wait(), timeout=1)
         yield f'http://localhost:{port}/xyz'
     finally:
         server.cancel()