Mind testing something for me just in-case?
Could you create a simple desktop flow with a 20 minute wait inside it and just tell your flow to run that unattended on that server? See if that procures the same time-out error, that would kill any notion that this could be desktop-flow related.
If you do indeed get the same thing, I'd recommend trying to use the following:
(Note you haven't mentioned any of the following that you've used so I assume you haven't)
-Send Mouse Click with move mouse to x,y (0,0) with high speed animation at some point in your flow
-Send Keys with text as hardware keys enabled (Try something like ALT+Tab, maybe that will work)
-Otherwise you're gonna have to talk to your IT team about potentially removing the 15 minute idle restriction or just provisioning a separate VM
Hope this helps somehow.