I've never heard this, but I surmise that it's been around a long while.
To remind people, and inform the young, 5.25inch (and 8 inch) floppy disks were genuinely floppy. 3.5 inch ones, which I first saw around 1987, are not. To state the obvious, 3.5 inch ones are only called 'floppy' because they fulfil the same function as the older varieties.
I suppose someone decided not to separate words and meaning in this way and so coined the term 'stiffy'. I'd have more expected it from the Australians, but - hey- who said the world had to work the way I expected it?
Does 'stiffy' have a sexual connotation in South Africa?