OK, if you are looking at a list of files and you see
  console.log
  console_servername_date1_time1.log
  console_servername_date2_time2.log
  console_servername_date3_time3.log
  console_servername_date4_time4.log
And you know that the server is down right now because it ended abnormally, which one do you look at?
Me, I would look at console.log and see what the last entries are.
IBM, would look at one of the earlier ones and tell you that the reason it is down is because you typed in quit.

;-)

----edit----

In hindsight, that was probably not very kind of me to say. But I've (also) noticed that Domino support, which was once the very definition of excellence, is nowhere near that now.

If no NSD is being generated, I would wonder if there is an OS, storage or memory issue. For example, does storage on the data volume go read only when Domino hangs or crashes? Is this a VM or physical server? If VM, that would be another layer to consider. 

Has support asked you to start Domino with the ServerTasks= line in the Notes.INI quoted out? 

I am an IBM i guy.  Forced to move some Domino servers to the world of Windows.

Apparently this is a no-no.
- Log on to Windows server with Remote Desktop.
- Start Domino server as a Windows Service.
- Test.  Works fine.
- Log off of Remote Desktop
- Server dies hard.
Now I guess I've figured out why the server dies right while I'm trying to go home...

Ok.  Restarted Remote Desktop.
Two services said they were Running:
- IBM Domino Diagnostics (CProgramFilesIBMDomino)
- IBM Domino Server (CDominoData)
I stopped them.  I had to stop them individually, they didn't seem to be tied together.
I started IBM Domino Server (CDominoData).
Then I started IBM Domino Diagnostics (CProgramFilesIBMDomino).
I was able to connect from a Notes client.
Then I logged off of Remote Desktop.
I was still able to connect from a Notes Client.

All good now.

I had to migrate a stable Domino server off of IBM i on to Windows so that I could add Trend Micro's Scan Mail for IBM Domino.

I've lost all stability.  It's a rare day that the Domino server will last 24 hours without crashing.  No nsd file is generated.  I have a ticket opened with IBM, 01580,082,000, but it's like pulling hen's teeth to get anywhere with them.

Do not just click on the desktop icon "IBM Domino Server" to start it.  Even if you say start it as a service when you log off the service dies.

I've done some things with the service "an' stuff", and Windows' own limitations are a bear for this.

If you're still having trouble, is the service running under SYSTEM account?

If not, the account you're running it under, it needs a privilege allowing it to store its password & if it's doing something special like connecting to a share drive, it needs a few other privileges to reach out there and authenticate with the other side.

We're good.  You just have to start the service from Services in Control Panel and not from the desktop icon.  The desktop icon is no good, even if you select start as a service.