There will always be a means of exchange that is generally accepted by the people because of the complexity of want and desire. Duration will face the challenges faced by trade by barter. Which is basically, want and desire.
Unlike movies, you can't give somebody your time
Well, in fact you can (like in conversations or whatever), but there's no guarantee that anyone will be interested in your precious time at all (and it is more like spending time, not earning it). In this manner, there cannot be what we could loosely call a universal time or duration exchange. In other words, duration is not fungible, i.e. any unit or part of duration is different from another unit, and therefore it cannot be used as money
See, one bitcoin is still the same bitcoin no matter what wallet it came from. Technically, it is not quite so due to tainted coins (wallets) but it is still a safe assumption overall (and you can always use mixers if something). To sum it up, the whole idea seems to be stillborn as it has severe issues with fungibility, which makes duration not suitable to be used as money, end of story