The next step is probably to see how much of Duplicati starts. You can practice with manual start and stop, sorting processes alphabetically in Task Manager (Sysinternals Process Explorer gives a better view), then seeing what processes beginnning with Duplicati come and go. One reason for the server not staying up is that Windows by default only allows a service 30 seconds for start. Duplicati does a huge amount of disk reads at a time when a system is stressed with everything else trying to start up. Delayed start puts it in a later group, but it might still not be enough if your disk is still overloaded then.
Windows service not starting - “Service did not respond in time” message shows how to raise timeout, however it’s a registry edit and also has a limited range. Possible the maximum is 120. I’m not certain.
Windows Service fails to start #2717 is further technical explanation behind what might be happening.
If we can determine from your process watching that the issue is Duplicati not being able to validate an update quickly enough despite all adjustments, you can go to not using the updater mechanism, but to always install updates by hand from a .msi after uninstalling the previous Duplicati. This keeps settings.
Do you know if you are running a Duplicati-installed update? Some places to check are in following link: