A few years ago, I noticed that a lot of plants along my fence were dying. I am quite sure it was due to the neighbor using a lawn service that used weed killers. Some of my goldfish also died after the lawn service man did his thing. I told the neighbor I wanted to be there the next time that man came. He never showed up!
If you have an Extension Service in your area where you could send or take a soil sample would also be helpful.

If we need to plant something on the hill to replace the ice plant that died, should we just use ice plant again, or is there something else you can suggest? And if we do plant ice plant, how do we do that? Do we buy seeds, or do we just cut some off of the remaining ice plant and plant those cuttings in the bare areas on the hill? Thanks again for any suggestions.

There's a possibility that your ice plant is just dying of old age. You can easily replant with cuttings. Cut off some newer growing plant ends - long enough to get at least two leaf nodes sections underground. Pinch off the leaves on the underground part of the cutting and just stick it in the ground. Spray the cuttings daily for a few weeks or until it is obvious they are doing well. Ice plant cuttings grow really well. You might consider buying some other colors of ice plant and making the hillside more interesting. I don't envy the amount of work it will take to remove the old ice plant but if it's dead - it's dead . . . and should be removed.