According to your log file the backup was successful, all backup parts were uploaded to Dropbox, old files were removed from Dropbox and the backup archives which have already been transferred to Dropbox have been removed from your server.
The problem you have is that Watchful.li expects a newer version of Akeeba Backup with a slightly different JSON API than the ancient version you have on your outdated Joomla! 1.5 site. As a result, it gets stuck on the last step of the backup process until it decides to stop trying.
Unfortunately, this is something which cannot be fixed. Actually, it is something which HAS been fixed, but not for Joomla! 1.5. Since the version you are using has been end of life for two years we won't provide any update to it. The good news is that your backup DOES WORK, it's Watchful.li which doesn't see that it did work.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
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