Session idle timeout disconnects during long-running background tasks

Problem

Claude Code sessions disconnect after a period of idle input, even when background tasks are actively running. This forces users to babysit sessions during long-running workflows instead of kicking off work and walking away.

Reproduction

1. Start a Claude Code session
2. Kick off a long-running background task (e.g., run_in_background: true on a 15-30 minute build)
3. Walk away from the computer
4. Return to find the session disconnected — background task results lost

Real-World Workflow This Breaks

User: "Build iOS app, submit to TestFlight, then deploy backend to staging"
Claude: Starts EAS local build (15-30 min) in background
         ...user walks away...
         ...session disconnects after idle timeout...
         ...build finishes but no one is there to run the submit step...

This is especially painful for:

• EAS/Xcode local builds (15-45 minutes)
• Waiting on CI/CD pipelines to complete before next step
• Docker builds on remote servers (5-15 minutes)
• Multi-step deployment workflows where each step depends on the previous
• Cursor Agent dispatches that take 5-20 minutes to complete

Expected Behavior

At minimum, one of:

1. No idle timeout while background tasks are running — if Claude Code initiated a background task, keep the session alive until it completes
2. Persistent background task results — if the session does disconnect, the results should be available when the user reconnects or starts a new session
3. Configurable idle timeout — let users set their own timeout (or disable it) for long-running workflows
4. Session resume — ability to reconnect to a previous session and pick up where it left off, including pending background task results

Environment

• macOS Darwin 25.3.0 (MacBookPro16,1)
• Claude Code CLI
• Workflows involve: EAS builds, Docker remote builds, GitHub Actions monitoring, Cursor Agent CLI dispatches

Workaround

Currently the only workaround is to chain everything into a standalone shell script that runs outside Claude Code, which defeats the purpose of the orchestration capabilities.

Impact

This is a significant workflow blocker for developers who use Claude Code as an orchestration layer for multi-step, long-running development tasks. The whole value proposition of background tasks is diminished if you have to keep actively interacting with the session to prevent disconnection.