In a small way it's already happened. I worked on a large corporate document project in 1990 and 1991. The documents were written in Microsoft Word 1.0. Graphics were created in MicroGraphx Designer. Some graphics were create in tools (names unremembered) running on DOS. None of this material is usable today. The latest version of MS Word doesn't recognise these old DOC files. There is no support anywhere for MicroGraphx Designer files. The DOS software is long gone. I still have printed copies.
There's also the point that we may not know what will be interesting or relevant in the future.
So when people go to the British Library to see the four remaining copies of the Magna Carta, now 800 years old, they might like to wonder whether current "digital only" records, personal or corporate, might be readable by someone in the year 2815!!!! In my experience, it's only taken twenty-five years to render some digital files close to unrecoverable.