diff --git a/gate/github.py b/gate/github.py
index b27c6a60..f87befa1 100644
--- a/gate/github.py
+++ b/gate/github.py
@@ -95,7 +95,10 @@ def _wait_for_connectivity(max_wait: float = 30.0) -> bool:
                 s.close()
             except Exception:
                 pass
-            time.sleep(min(2.0, deadline - time.monotonic()))
+            remaining = deadline - time.monotonic()
+            if remaining <= 0:
+                break
+            time.sleep(min(2.0, remaining))
     logger.warning(f"GitHub unreachable after {max_wait}s of probing")
     return False
 
diff --git a/tests/test_github.py b/tests/test_github.py
index 6111232e..af19dfe8 100644
--- a/tests/test_github.py
+++ b/tests/test_github.py
@@ -1,8 +1,10 @@
 """Tests for gate.github module."""
 
+import socket
 import subprocess
 from unittest.mock import patch
 
+from gate import github
 from gate.github import (
     _build_comment,
     _format_build_section,
@@ -16,6 +18,34 @@
 )
 
 
+class TestWaitForConnectivity:
+    def test_timeout_does_not_sleep_negative(self, monkeypatch):
+        class FakeSocket:
+            def settimeout(self, _timeout):
+                pass
+
+            def connect(self, _target):
+                raise TimeoutError("timed out")
+
+            def close(self):
+                pass
+
+        times = iter([0.0, 0.0, 6.0])
+        sleeps: list[float] = []
+
+        monkeypatch.setattr(
+            socket,
+            "getaddrinfo",
+            lambda *_args, **_kwargs: [(None, None, None, None, ("127.0.0.1", 443))],
+        )
+        monkeypatch.setattr(socket, "socket", lambda *_args, **_kwargs: FakeSocket())
+        monkeypatch.setattr(github.time, "monotonic", lambda: next(times))
+        monkeypatch.setattr(github.time, "sleep", sleeps.append)
+
+        assert github._wait_for_connectivity(max_wait=5.0) is False
+        assert sleeps == []
+
+
 class TestFormatFindings:
     def test_empty_findings(self):
         assert _format_findings([]) == ""