Near end cross talk (NEXT) saturates because the coupled signal or energy propagates backwards on the victim trace back towards the source.
For a trace longer than the rise (or fall) time of the signal, each segment of trace, or each transmission line segment couples to the adjacent trace, but in different locations. So the individual coupled pulses from different segments of the trace reach the near end (source) at different times. The net results is that the NEXT is stretched out in time, but at a constant amplitude.
The text "High-Speed Signal Propagation (Advanced Black Magic)" by Drs. Howard Johnson and Martin Graham does a good job of explaining this, on pages 318-321.
Added graphics and some more detail
The picture below tries to illustrates this problem.
Red shows the leading edge of a signal on the aggressor trace as it propagates along the trace. Blue shows the coupled noise pulses on the victim trace.
These pulses travel both left (towards the source) and right (towards the destination) along the victim trace. At the destination end (far end), the pulses all arrive at approximately the same time and so add in magnitude. The longer the traces, the more pulses there are to add , which is why the FEXT increases with trace length.
At the source end (near end), the pulses arrive in a time sequence fashion, P0, then P1, P2, etc. So at the near end, the crosstalk signal increases in time with trace length, but not amplitude (once it reaches its nominal value).
Keep in mind that this is not a discrete phenomenon as the graphic might suggest. The coupled pulses are continuous along the length of the victim trace, occurring spread out in time as the signal edge propagates down the aggressor trace.