Kiro/Amazon Q CLI - Is there any way to resume the task on the specific part it stops?

Yes, Amazon Q Developer CLI now offers conversation persistence features that can help you resume where you left off. With the q chat --resume command, your conversations are automatically saved by working directory, allowing you to pick up exactly where you left off when you return to a project.

Additionally, Amazon Q Developer has added two specific commands to give you more control over conversation states:

• /save - This allows you to explicitly save the current conversation state
• /load - This lets you restore a previously saved conversation

These features are designed to help manage multiple conversation threads related to different aspects of your project. You can save a conversation about one feature or task, switch to something else, and then load the previous conversation when you're ready to continue.

This should help with your issue of having to restart from the beginning after encountering throttling errors, as you can save your progress before potential throttling points and then resume from there if needed.
Sources
Exploring the latest features of the Amazon Q Developer CLI | AWS DevOps & Developer Productivity Blog