If you've had a system crash, reinstall, or other circumstances have forced you to reinstall Hamachi without its original configuration, you will receive a new Hamachi Client ID when you reinstall the software. This Client ID does not retain your IP address or original network ownerships.
This issue can be prevented by making a backup of the Service Configuration folder, which can be found under System > Preferences > Settings > Advanced Settings. Scroll to the bottom of the page, and highlight the Service Configuration entry and click Open. Copy the contents of this folder to a safe location, and anytime you need to reinstall, you can copy the files back.
You can use the My Networks page on the LogMeIn site for free. This allows you to create and manage networks from the web. This will prevent you from having to perform this backup, or worrying about a system crash.