Length Contraction Should not be Independent of Time

In Special Theory of Relativity it looks that the length contraction along the direction of the motion is independent of time, i.e. if a rocket flies one second, or the rocket flies one year the rocket's along-the-motion length contraction is the same, since the contraction factor \[ C(v)=\sqrt {1-\frac{v^{2}}{c^{2}}} \] depends on the rocket's relativistic speed ($v)$ and on the light speed in vacuum ($c)$ only. \newline We find this as unrealistic, incomplete. It is logical that flying more and more it should increase the length contraction. What about the cosmic bodies that continuously travel, do they contract only once or are they continuously contracting?