Some of the commenters on my last post pointed out that time travel itself is not problematic - after all we travel through it, day by day, all the time. The problem is the discontinuity. Can one and the same thing 'jump' from one point in time to some future point in time without existing in the time in between? If so, then since it does not exist at the point just after which it has jumped, and begins to exist again after it has landed. This seems to violate Locke's maxim.
Some further points to consider. Dr Who's time actually isn't discontinuous. He steps into the Tardis, fiddles about with the dashboard and that glass thing that goes up and down, and waits. Then he opens the door onto a different time, far in the future perhaps. From his point of view, there is no discontinuity, which only exists from the point of view of someone outside the Tardis.
It's the same with sleep (by which I mean deep sleep). My consciousness does not exist during sleep. But there is no apparent discontinuity on my side. I turn out the light, think of sheep, and then the next thing I know there is light underneath the curtains. Consciousness in its very nature is continuous, and (as I argued in a series of posts around here) it is finite.
A further problem. In what sense am 'I' asleep, or unconscious? If I am my consciousness, and if my consciousness ceases to exist when I am unconscious, how can I be said to be asleep, or unconscious?