It could be a fungus of some sort--if that's the case, there are going to be fungal spores in all sorts of places on the plant even if a section still looks healthy, so when you transplant it to the new pot, the fungus goes right along with it and will grow and eventually make your new plant have the same problem as the old one. Next time you transplant, get rid of as much of the old soil as possible, then give the roots a swish in a dilute hydrogen peroxide solution, and you may want to swish the leaves in it too, or spray them with the peroxide solution or some other antifungal. Then put it in the clean soil in the clean pot, and the problem should stop. Also be careful how much you're watering them, too much water will encourage fungal growth (and no matter how careful you are, there are often mold spores in the air, or maybe there's one or two that survive the peroxide treatment, and if you give them an overly moist environment to grow in, the problem can come right back)
It also could be just older parts of the plant dying off--if you have a lot of new growth on the top, some of the older growth underneath will tend to die off. I'm not familiar with this particular plant so I don't know how it grows, but I know I've seen this on some other perennials that I grow. If this is what's happening, you can just pull out the dead unsightly parts.
Do the leaves get spots on them first, or get sort of soggy/wilty looking as they die? That would more likely indicate fungus to me, but if they get sort of crispy and brown and dried up looking, then it could just be older foliage dying back.
