Well, almost one month on but I've resolved the issue and wanted to leave a record in case this discussion turns up in someone's search for 'Previous Shutdown Cause: -2'.

The problem was caused by some replacement RAM; I'd upgraded the 4GB that came with the Mac Mini to 8GB from Crucial. When I swapped the original RAM back in, the restarts stopped happening. (I repeated the tests with the original RAM and Crucial RAM a few times to make sure it wasn't just a seating problem.)

Bear in mind that the RAM passed Apple's diagnostic tests and several runs of memtest. To be honest I didn't expect the Crucial modules to cause a problem as their products have always worked flawlessly in all the memory upgrades I've performed or helped with.

Anyway, the evidence suggested otherwise, so I RMA'd the RAM with Crucial (great service as always), and the replacement DIMMs are now in the Mac, which hasn't restarted of its own accord for about a week