### Check for existing issues

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

### What happened?

**Issue summary**

When using a hosted_vllm model backed by vLLM, continuous chat works correctly in the LiteLLM Playground, but fails in /ui/chat starting from the second user message.

The first message succeeds, but on the second turn /ui/chat returns this error: ``` Error occurred while generating model response. Please try again. Error: Error: 404 litellm.BadRequestError: Hosted_vllmException - {"error":{"message":"Response with id 'resp_998bca5d44e22037' not found.","type":"invalid_request_error","param":"response_id","code":404}}. Received Model Group=Qwen/Qwen3.6-35B-A3B-FP8 Available Model Group Fallbacks=None ```

**Observed behavior** - LiteLLM Playground: multi-turn chat works - /ui/chat: first message works, second and later messages fail with response_id not found

**vLLM startup parameters** ``` Qwen/Qwen3.6-35B-A3B-FP8 \ --quantization fp8 \ --tensor-parallel-size 2 \ --reasoning-parser qwen3 \ --host 0.0.0.0 \ --port 8000 \ --dtype auto \ --gpu-memory-utilization 0.95 \ --max-model-len 262144 ```

**Suspected is…