It would be best to plant another type of ice plant or a different ground cover. If you replant the same ice plant, it may grow well for a while, but could die later if there is a pathogenic fungus in the soil.
Certain water-mold fungi can infect and kill the roots of ice plant. This usually occurs on poorly drained soil after a prolonged period of heavy rain or excess irrigation. The disease frequently damages the small-leafed ice plants like Disneyland and rosea (Delosperma and Drosanthemum sp.). Red apple ice plant (Aptenia cordifolia) and Freeway ice plant (Carpobrotus edulis) seem to be more resistant to soil pathogens.
Water mold fungi like phytopthora which damage plants can survive in soil for many years. Fungicide products labeled for the control of foliar diseases are not effective against soil born fungi. The best course of action is to grow resistant plants and irrigate carefully to avoid excess soil moisture.
For more information see UC IPM Pest Note 74133 Phytopthora Root and Crown Rot in the Garden
By V. Lazaneo, Urban Horticulture Advisor, Emeritus, UC Cooperative Extension, August 2012