I will reframe the question::
Is there a term for "stability" of a equilibrium point, where all the trajectories stay a steady distance away from the eq. pt.?
Answer::
Sometimes such an equilibrium points is called a "marginally" stable eq. pt. Please refer to the following links.
http://en.wikipedia.org/wiki/Mechanical_equilibrium
and
http://hebb.mit.edu/courses/9.641/2000/lectures/lecture10.pdf