Thermal conductivity measurements show that ice continues to amorphize for several days when kept at a fixed pressure p in the 0.79-0.88 GPa range, and fixed temperature T in the 127-130 K range. Thermal conductivity kappa decreases according to a stretched exponential in time, and its limiting long time value kappa(infinity) varies with p and T. At 0.8 GPa and 128 K, kappa(infinity) remains 2.5 times the value observed for high-density amorph. Consequences of these findings for our understanding of amorphization are discussed. (C) 2004 American Institute of Physics.