I have seen some orgs have this issue, and the way it's normally handled is exactly what you've done which is to trigger outlook to start up before using actions that don't work when it's closed. However, the strange thing is that I'd assume none of the actions would work for you.
As for the right solution to this, I don't know that I've personally witnessed the solution unfortunately. I would suggest testing this on multiple machines, and even try it at home on a personal computer if you have a license you can use at home (like a training/partner/etc. license or maybe if you use the learning edition or something). I imagine it's possible that the action is correctly trying to trigger Outlook to open its background instance but that something is blocking it from succeeding. Maybe antivirus? The code stages between, for example, 'Internal_Get Items' and 'Save Attachments' seems like it'd indicate, as Eric suggested, that all of the actions are triggering that background instance of Outlook to open.
Also, I just noticed that this post was originally in January and that you've been dealing with this for a little while. You may want to submit a Support Ticket to Blue Prism and see if BP can help troubleshoot more. I suspect there's a solution but it might just be difficult to find.
Dave Morris, 3Ci at Southern Company