Please try installing the Akeeba Backup Professional 4.1.0 stable package twice in a row, without uninstalling Akeeba Backup before, in between or after.
This is a Joomla! bug we've identified since the early Joomla! 1.5 days but for various reasons it never got fixed. We are currently working with other core contributors to get all those extension installer bugs fixed in Joomla! 3.4.0 and –whatever doesn't make the 3.4 release– Joomla! 3.5.0. In the meantime the install twice workaround seems to be working on the vast majority of cases. Please let me know how it worked out for you.
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!