You did not state which version of Outlook/Office you are using. I am using Outlook 2016/Office 2016, and I am not having any issues with it (although I have no need to backup individual EMails/EMail "folders"). Yesterday I posted information about the latest version of Office 2016 (and thus Outlook 2016). I'll repeat that link here for you:
https://support.office.com/en-us/ar...542-9954-7e3209681a41?ui=en-US&rs=en-US&ad=US
Outlook 2016/Office 2016 is the only one that Microsoft is continuing to update/support.
Also, what
exact Mac Book Air model do you have? I have a mid 2013 13" Mac Book Air, with a 252 gig SSD, and it works fine.
And why did you "upgrade" to High Sierra? There are still a fair amount of issues associated with High Sierra, at least from posts I have seen here. I am still using Sierra, OS 10.12.6, and it is as stable as ever. And as of now, there are no major "advantages" for me to upgrade (besides, I am still waiting for a upgrade for Tech Tool Pro for High Sierra compatibility).
By the way, are you aware of how to permanently remove deleted EMails from Outlook 2016? I do that just about every day, and it helps to keep my EMail "stuff" manageable.