#24929 [Bug]: Streaming responses fail in bursts aligned with httpx client ttl
### Check for existing issues
- [x] I have searched the existing issues and checked that my issue is not a duplicate.
### What happened?
I have LiteLLM Proxy deployed (self-managed) and use it for streaming completions via /v1/messages endpoint. The client uses anthropic.AsyncAnthropic => proxy => Vertex. However, the client observes periodic large spikes of httpx.ReadTimeout errors. Timeouts spike every 3600s, which matches _DEFAULT_TTL_FOR_HTTPX_CLIENTS. When I monkeypatch this TTL in my proxy deployment to 5400s, the spikers shift to every 90m, conclusively implicating the httpx client TTL mechanism in this bug.
Spikes in client-experienced httpx.ReadTimeout with default settings (TTL is 60m) <img width="697" height="339" alt="Image" src="https://github.com/user-attachments/assets/39a2bc35-a524-410d-b19e-a985c6fc9bc3" />
Spikes in client-experienced httpx.ReadTimeout after TTL is monkeypatched to 90m <img width="699" height="338" alt="Image" src="https://github.com/user-attachments/assets/0c03fe24-278a-4d94-8dd9-0dda329412b7" />
Note that we confirmed that the center of the spikes is aligned with exactly the minute that a new revision of the proxy service was deployed. So …