Actually, the solution is to shut it down but don't remove power. Most OSes will let you do this, and as long as APM/ACPI/whatever isn't used to power the box down, all the BIOS knows is that it was still supplying power when it went away.

I haven't done this with Linux in a long time, so I don't remember what the exact solution was, but it did exist. Even if I did remember, actually, it'd probably be so different now as to be irrelevant.

FWIW, the halt(8) man page says that it'll power off on "halt -p" or "poweroff", but shouldn't on just a "halt". Check your power management scripts to see what it's calling to halt the OS. It may be calling a script that tries to power off at the end instead of letting the machine run.