I'd imagine you'd have to do a task (like inputting a passcode) every so often or the drive would be made inoperable.

For SSD's it'd be as simple as an automatic single pass overwrite and a new encryption key. For HDD, the hyper-paranoid could rig their drives with small explosives to fracture the platters.

^This. In fact you can buy readymade solutions now which physically destroy the NAND gates on the input of a code, or as you say, if you fail to input a code within a time limit.

An example I've given here before is: http://securedrives.co.uk/

There are other solutions though, and of course you can make your own if you feel confident about it.