Remote control reconnection fails permanently after iOS connection drop

Description

When using remote control from the iOS Claude app to control a CLI session, if the iOS app suspends or the network connection drops, the CLI session enters a "Remote Control reconnecting..." state and never successfully reconnects. The only recovery is to manually kill the reconnect and re-establish from scratch.

Steps to reproduce

1. Enable remote control on a CLI session
2. Connect from iOS Claude app
3. Issue a few commands successfully
4. Switch away from the Claude iOS app briefly (or experience any network interruption)
5. Return to the iOS app — it shows no response
6. CLI session shows "Remote Control reconnecting..." indefinitely

Expected behavior

• The CLI session should detect the dead connection and either:
• Successfully reconnect automatically, OR
• Time out after a reasonable period and return to a "waiting for connection" state so a new connection can be established from iOS

Actual behavior

• CLI hangs in "Remote Control reconnecting..." forever
• Requires manual intervention (Ctrl+C or /remote-control) to reset
• iOS side gets no feedback that the connection was lost

Context

iOS is particularly prone to this because the OS aggressively suspends background apps and kills their network connections. A resilient reconnection strategy (exponential backoff with a max timeout, then fallback to "waiting for new connection") would make the mobile remote control experience much more reliable.

Environment

• CLI: Claude Code on Windows 11
• Remote: iOS Claude app
• Connection drops consistently after iOS app backgrounding or WiFi/cellular handoff