Domain account has full control.

System account has full control.
Local account has no control. I originally asked our server team for this access to be granted but wouldn't (against policy) and advised to install with domain account as it was "a replica" of the local account.

Should have gone with my gut instincts.
This explains why the local account has the least amount of processes starting.
It doesn't explain why SYSTEM can't start the app though. From what I can see, it has the same privs as the domain account and more.

The other question I have is when using a network share, what user does OBIEE connect to it with? Is it the install account?
If so, could the application server be dropping it's connection to the network share when the domain user is logged off?

As Christian mentioned, maybe I should bite the bullet and reinstall but even if I did that, the local account won't be granted access to the share and therefore, it'll result in the same issues.

Aha.... I may have mapped using the domain account.
If I map using the local account, then the connection shouldn't drop when the domain account is logged out.

Thanks for the light bulb moment Michael! Will let you know how I go.

Ok, i've worked this one out and it's more to do with my own stupidity that this didn't work in the first place.

Firstly, to your point Michael, I discovered that the app connects to the share using the user/pass of the user who starts the app and not who the share is mapped as.

In fact, you can disconnect the share mapping completely and the app will still work as it's connected on start up via the singleton directory specification in FMWConfig/bienv/bi-environment.xml.

This morning I tested starting the app using the task scheduler, running the task using the domain account (install account) and ensuring "Run whether user is logged on or not" was ticked. I then had all the domain sessions on that server ended and wallah.... app continued to run.

My 2nd test was to start the app manually by opening up the command line and physically typing "start.cmd" using the domain user. After the app was up, I had the domain sessions ended and wallah.... app had died!

So after all this, I should have clued on to the fact that you can't manually start the app and expect it to continue to run once that user had logged off.

Thanks both Michael and Christian for your help on this. I'm not sure there's a best answer unfortunately.
Perhaps you could both advise who to assign best answer to?