After a lot of experimenting, I can report that the reason for my Lenovo T400 shutting down while running Workstation was overheating of the GPU (and possible the CPU). What started as an intermittent problem got progressively worse, to the point where I was ready to go and buy a new laptop.
There is some excellent advice on the Lenovo community site, as it appears the Lenovo T400 has a habit of overheating :-( The best solution appears to be a tube of Artic Silver 5 thermal grease, and doing a better job than Lenovo of thermally bonding the CPU and GPU to the heatsinks.