What happened?

Current behavior

JSONRPCApplication always builds EventSourceResponse with Starlette’s defaults (src/a2a/server/apps/jsonrpc/jsonrpc_app.py:323). When an agent pauses longer than the default send_timeout, the next write raises SendTimeoutError, the response task exits, and the client never receives the remaining events. Long-lived agents tasks hit this path while waiting on external work.

Expected/desired behavior

Developers using the SDK should be able to configure a larger timeout or disable it entirely without subclassing the server. Semi-idle agents should keep their SSE channel open, even if send() occasionally blocks longer than five seconds.

Proposed fix

1. Add a stream_send_timeout: float | None option on JSONRPCApplication (plumbed through A2AStarletteApplication/A2AFastAPIApplication) and pass it to EventSourceResponse(...). Preserve the current default when the option is omitted.
2. Allow per-request overrides via ServerCallContext.state["stream_send_timeout"] so specific handlers can raise/lower the ceiling.
3. Document the new control (and the failure mode) in the SDK guide, recommending that long-running agents either disable or adjust the timeout, or emit frequent heartbeat events.

Relevant log output

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