I tend to leave them. Like most floaters, this plant once established tends to spread rapidly, and I toss out some of it pretty much every weekly water change. Sometimes it is the older plants, sometimes not; any with yellowing leaves I tend to remove first. I suspect this plant grows so rapidly the yellowing leaves are simply due to the nutrients being used up.
Oncve the daughter plants have leaves and roots, I doubt they obtain any nutrients from the parent plant. Most aquatic plants are like this. So separating them should not cause any issues. I find the very delicate "runners" often break just from the water change activity.