### Check for existing issues

- [x] I have searched the existing issues and checked that my issue is not a duplicate.

### What happened?

When a model has a long time-to-first-token, the proxy's SSE response sits completely idle. Reasoning and extended-thinking models routinely think for 30-120 seconds before emitting anything, and during that window the proxy writes zero bytes to the client.

Any hop between the client and the proxy that watches for idle connections then closes a connection that is perfectly healthy. AWS ALB defaults to a 60 second idle timeout, nginx to 60 seconds, Envoy to 300. The client sees a truncated or reset stream while the upstream request was still on its way and would have produced tokens shortly after.

Expected: while a streaming response is connected but has not yet produced its first token, the proxy should be able to emit something that resets client and intermediary idle watchdogs, so a slow-TTFT stream survives and delivers its tokens once the model starts responding.

Actual: nothing reaches the wire until the first real token.

The keepalive settings LiteLLM ships today look like they cover this and do not. AIOHTTP_KEEPALIVE_TIMEOUT, AIOHTTP…