I would just remove those dead areas. I've had that happen occasionally, and it never caused a problem. I think I've only lost one whole plant, and I've had a LOT of them. Sometimes they just run out of steam, I think. I've had one die right in the middle of two others, and they all received the same care. I've never fertilized mine. They seemed to thrive on just some water, so I never bothered. Some of mine got huge anyway, and I was afraid to fertilize!
I did end up breaking pieces off from the outside, and they rooted just fine. Maybe you can try that if you are afraid of losing the plant. I put them in pots in mostly shade, because it was so hot. They were later planted into the garden and didn't miss a beat!
