Why time difference is permanent and mass increase is temporary? When a clock is transported here and there into space and then brought to the same place it differs with the other clock.
When particles are accelerated with high speeds and then brought to rest their mass again gets back to its original rest mass.
Why?
Answer allegorically please.
 A: Because a clock record time, while your mass is just a physical property of your body.
To be clearer : 
You have two clocks that tick every second. They indicate 10:00.
You put one (clock A) into movement. As seen by clock B, the frequency of clock A will be different. It will tick every 1/2 second, for instance. Put clock A again at rest next to B. Clock A will eventually indicates 11:00 and clock B 12:00. But one hour later, clock A will indicate 12:00 while clock B shows 13:00. Got it ?
So the frequency of the clock will depend on its relative speed. The frequency will change if the clock is in movement, but will be back to the same value as before if you bring it back at rest.
A: Because time is accumulating, to calculate the time lapse, you integrate. The elementary time interval transforms like mass. The difference is that the total time lapse is done by "summing" over all elementary intervals. For the mass, you don't do this.
For mass:
$$m=\frac {m_0} {\sqrt{1-\frac{v^2}{c^2}}}$$
For time:
$$dt=\frac {dt_0} {\sqrt{1-\frac{v^2}{c^2}}}$$
$$t=\int{ \frac {d t_0} {\sqrt{1-\frac{v^2}{c^2}}}}$$
A: I think you mix up time (ie what this or that clock is showing right now), and time's speed (ie, how fast that clock is "ticking" compared to how another clock (possibly moving differently) is "ticking", as seen from a reference point.).
Like the first answer says, you should compare m with dt (time's "speed"), not t (ie, current time, the integration of that dt)
What changes when you move a clock in regard to another is that it's time's "speed" and its mass are changing, then go back to "normal".
The "current time" of the clock you are moving has changed "less" if you compare it to another clock "at rest". The clock that was moving will have, while moving faster, a slower "time speed", or "ticking rate", and then that "time speed" goes back to normal when it comes back to "rest" (compared to the reference clock). The accumulated time is therefore different, and will surely not "go back" (Going from T1 to T2

Of course this is all kind of mind boggling as the very word I used (ticking, backwards) are defined "in time", so it's kind of hard to separate whatr's physically happening from false information derived from the words themselves...
A: I dont think that's true.
Particles are constantly emitting radiation, and when a particle is moving at high-speed it emits less radiation and it also has a longer period of decay, so a high-speed particle loses mass at an inferior rate than when it was stationary, but still loses mass. You cannot stop a particle from decaying, and its rest-energy will never get 'unchanged'.
