Absolute time can be represented by a geometrical straight line T. Points on T correspond to moments, while distances to durations. The idea behind absolute time is that every event can be mapped to exactly one point on this single T, because there exist absolute temporal relationships among events.
However, time dilation revealed that the coordinate time of any one inertial frame is not absolute time, since both simultaneity and duration are inertial frame dependent. To be precise, from the perspective of absolute time what was demonstrated is this: when two inertial frames are moving relative to each other, it cannot be that the coordinate time in both of them measure absolute time. Yet the principle of relativity suggests that the situation of the two inertial frames must be symmetrical. It would not fit in the picture if it was possible that the coordinate time in one frame is absolute, while in the other it's not… and to make matters worse, there would be no known way to tell which frame is which.
This is the point where we must realize that time dilation has left us with no tangible evidence but only one thing supporting the idea of absolute time: our imagination, i.e. the intuition that we've gained from the limited spectrum of our day-to-day experiences. Time dilation has refuted the strongest argument we thought we had for absolute time. Namely, it's not true that two clocks always show the same time elapsed between any two of their encounters. To test this, we don't even need to define simultaneity and coordinate time, all we need is the two clocks.
That's why, since it does not seem to help to go back and try to adjust the simple and robust definitions that led us here, the choice has been made in special relativity to rather give up absolute time.