I battled with this issue for so long that I have now gone bald and have permanently fused with my computer stool. Hopefully others encountering the same issue find this thread before they succumb to the same fate.
The Steinberg Download Assistant uses a third party command line download manager, that many other applications also use, named aria2c.exe. Whilst most apps will only run this tool as and when needed, there are some applications that run this all the time. In my case, this was a RMM agent I have installed for my work.
The issue I was experiencing was because the RMM agent already had aria2c.exe running, so when the Steinberg Download Assistant ran the same executable and attempted to access the internet, it conflicted with the already running instance.
The fix? Simply search your running processes and shutdown any instances of aria2c.exe already running (you may need to disable a corresponding service to prevent it from restarting automatically). Once you have completed your Steinberg installation/upgrades, you can reverse what you disabled and move on with your day.
This may not be the fix for everybody, but hopefully it will help some.