When you reinstalled I hope that you did not uninstall first. As we have documented, the default backup output directory is in administrator/components/com_akeeba/backup. Joomla! does a stupid thing when uninstalling the component: it removes that directory and all of its contents, essentially deleting your backups. That is why we always advise to:
1. Use a backup output directory outside the web root
2. Never, ever, under no circumstances keep only one copy of your backups on your site. Ideally, keep three copies to be on the safe side.
3. Never, ever, uninstall Akeeba Backup unless you don't want to use it any more. Upgrading or refreshing the installation is as simple as going to the extension manager and install the Akeeba Backup package without uninstalling the existing release.
If you did not try to uninstall the component, your backups will most likely be in the default output directory I mentioned above.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!