It seems to be working now.

* Changed it use UNC (ie. \\Servername\Sharename) rather than the drive letter (S:\Softrak\DataCare\DataCare.exe).

* "Run only when user is logged in" is selected and I disconnected rather than logged off.

Impressively, with "Wake the computer to run this task" selected, it actually wakes my computer up out of sleep and runs the task.

I'll keep an eye on it this week but so far so good!