I had this problem at work as the result of a group policy that automatically locked all screens after 15 minutes of inactivity. It wasn't a problem while a test was running, but if I wanted to leave a screen unlocked for a nightly scheduled test I couldn't do it. I was able to request and get a specific exemption to this policy for my user account from our IT team. Perhaps your IT team won't go for this, or you may have to provide some sort of assurance that the unlocked screen is still secure (e.g. in a locked room), but it's worth asking.
FYI, I discovered a very useful trick related to this. I have dedicated test machines that I access via remote desktop, but want to disconnect the remote desktop session and still leave them unlocked for TestComplete. I discovered that if a monitor is connected to these machines, even if it doesn't have power (or even a power cord), you can still disconnect the remote desktop (using https://support.smartbear.com/viewarticle/86476/) and the machines will 'think' they have a local console and run the tests just fine.
