I believe time will cease to exist when man ceases to exist.
Except, time existed prior to man's existence.
That's proven either Biblically, or scientifically.
God created Man on the 6th day, so there were 5 days prior to that. And an unknown essence prior to the First Day, called "in the beginning," existed. With an unknown period for which that "beginning" stretched. Even the words used in Genesis 1:1 to 1:3 are interesting in this regard:
1 In the beginning God created the heavens and the earth.
2 Now the earth was [a] formless and empty, darkness was over the surface of the deep, and the Spirit of God was hovering over the waters.
3 And God said, "Let there be light," and there was light. 4 God saw that the light was good, and He separated the light from the darkness. 5 God called the light "day," and the darkness he called "night." And there was evening, and there was morning—the first day.
This "beginning" existed prior to the first day, and God created prior to it. Which mean that time transcends God's creation of the Universe (or at least the heavens and the earth). The verb choices in 1:2 are interesting, as well as the notion of "now." Day one doesn't start until 1:3 (day cannot happen until light exists, so the events of 1:1 and 1:2 happen before day 1), but we have the acceptance of a point in time ("now") as well as demarking this moment with a past tense verb.
Granted, it isn't aramaic or the direct thoughts of God and merely the English language... but I bet similar notions of time acknowledgement are present in the original copies of Genesis.
or:
Dinosaurs were around long before man was there to observe them. As well as many other species, or even lifelessness (comets, stars, etc can all be dated). Carbon dating allows for the existence of time flow, or radioactive decay of some sort (in the case of astral bodies).