Intermittent Dispatch Failure Errors in Q CLI

## Bug Report: Intermittent Dispatch Failure Errors in Q CLI

### Description

Amazon Q CLI frequently fails with intermittent dispatch failure errors, significantly impacting productivity. The error occurs randomly during usage, suggesting a service-side infrastructure issue rather than client configuration problems.

### Error Message

```
WARNING: Retry #2, retrying within 10.0s..
Amazon Q is having trouble responding right now:
0: Failed to send the request: An unknown error occurred: dispatch failure
1: An unknown error occurred: dispatch failure
2: dispatch failure (io error): an i/o error occurred: error sending request for url (https://q.us-east-1.amazonaws.com/)
3: dispatch failure
4: io error
5: an i/o error occurred: error sending request for url (https://q.us-east-1.amazonaws.com/)

Location:
crates/chat-cli/src/cli/chat/mod.rs:1146

Backtrace omitted. Run with RUST_BACKTRACE=1 environment variable to display it.
Run with RUST_BACKTRACE=full to include source snippets.
```

### Environment

- **OS**: macOS 15.7.1
- **Q CLI Version**: 1.19.6
- **Network**: Mobile hotspot, all other services working normally
- **Authentication**: Professional license

### Steps to Reproduce

1. Use Q CLI normally for extended periods
2. Error occurs randomly during usage
3. No specific trigger identified - happens intermittently

### Expected Behavior

Q CLI should maintain stable connection to Amazon Q servers and handle requests consistently.

### Actual Behavior

- Frequent intermittent dispatch failures
- Error pattern always includes `dispatch failure (io error)`
- Requires manual retries or session restarts
- Impacts productivity due to unpredictable failures

### Troubleshooting Attempted

- [x] Complete Q CLI reinstallation
- [x] Tried [Kiro CLI](https://kiro.dev/docs/cli/migrating-from-q/) (same failures occur)
- [x] Authentication reset (`q logout` / `q login`)
- [x] Network connectivity verified (other services work fine)
- [x] Re-booting Mac (!)

### Analysis

The intermittent nature strongly suggests this is a **service-side issue** rather than client configuration:

1. Configuration problems are typically consistent
2. All other internet services work normally on same network
3. No local configuration changes correlate with failures
4. Both Q CLI and Kiro CLI exhibit same behavior

### Impact

- **Severity**: High - significantly impacts daily productivity
- **Frequency**: Multiple times per day
- **Workaround**: Manual retries, session restarts (not reliable)

### Additional Context

- Error consistently points to network/IO issues with Amazon Q servers
- All other AWS services work fine on same network connection
- Issue appears to affect multiple users based on community discussions

### Related Issues

- **StackOverflow**: https://stackoverflow.com/questions/79825141
- **AWS re:Post**: https://repost.aws/questions/QUwgex4wvLS5eBdIVcGsHlsQ
- **Related GitHub Issues**:
- #1210: https://github.com/aws/amazon-q-developer-cli/issues/1210
- #2214: https://github.com/aws/amazon-q-developer-cli/issues/2214
- #1982: https://github.com/aws/amazon-q-developer-cli/issues/1982