Q:

Why isn't length contraction permanent even though time dilation is?

It's my understanding that when something is going near the speed of light in reference to an observer, time dilation occurs and time goes slower for that fast-moving object.  However, when that object goes back to "rest", it has genuinely aged compared to the observer.  It's not like time goes slow for a while, and then speeds back to "normal," so that the age of the observer once again matches the object.  The time dilation is permanent.  Why wouldn't the same thing happen with length contraction?  Since the two are so related, you'd think if one is permanent, the other would be also.  And from everything I've read so far, length contraction is not permanent.  An object will be at rest touching an observer, go far away near light speed, return to touching the observer, and be the same length it was at the beginning.  It shortens, and then grows long again, as if its shrinkage was an illusion the whole time.  Did I just not read the right things or what?  Were my facts gathered incorrectly?

A:

Time dilation is a comparison of rates. When an object is moving fast with respect to you, it's clock rate is slow, and when it comes to rest with respect to you its clock rate returns to normal. The time difference between the two clocks at this time is due to the accumulation due to these different time rates. That is the leftover effect of the time dilation but not the time dilation itself.
Length contraction, like time dilation, exists when there is relative motion and goes away when there is no relative motion, but there isn't any "accumulation" with length contraction, so there is nothing to be "left over".

A:

The way I see it, time dilation is the real effect here.
Length contraction (in SR) is just a consequence of the fact that the "length" of a rod is the distance between simultaneous positions of the rod's endpoints. But two observers with different velocities will have different ideas about what simultaneous is, and this means they measure different lengths.
The best paradox to think about here is the "ladder" or "train" paradox. I think if you have got your head around that you understand length contraction.

A:

It's my understanding that when something is going near the speed of
  light in reference to an observer, time dilation occurs and time goes
  slower for that fast-moving object.

According to the 'something', it is the observer's clock that runs slower and it is the observer's rulers that are contracted.  That is to say, the time dilation and length contraction are symmetrical.  Neither clock can be objectively said to be running slow and neither ruler can objectively said to be contracted.

However, when that object goes back to "rest",

Now the symmetry is lost; the object's accelerometer registered non-zero acceleration for some time while the observer remained inertial.  This means that there is now an objective difference between the object (non-inertial) and observer (inertial) and, thus, an objective difference in elapsed times.

Why wouldn't the same thing happen with length contraction?

In fact, in SR, acceleration of an extended object must be handled with great care.  If an object is to not to stretch or compress during acceleration, different parts of the object must have different (proper) acceleration.
See, for example, this question for additional information and links.

