The earth’s orbit and tilt are far form stationary.
http://en.wikipedia.org/wiki/Milankovitch_cycles
Says it better than I can.
I’m OK with orbits which are essentially eccentric. Up until Kepler, the orbits were expected to be perfect circles. Then Kepler showed that they were elliptical. Then we found out they were basically elliptical, but eccentric.
It just seems to me — and maybe I’m wrong — that if ice buildup were to increase the eccentricity, I do not see how a return to relative stability would be achieved. I would expect greater and greater degrees of eccentricity.