Q.Goosefoot plant
I brought back a goosefoot plant from UK 3 years ago. The plant was grown in water all the time when my late father had it and I kept it in water after I took over. However, about a year ago the plant started to look a bit sad. First of all, the roots were rotten and came off the plant. I washed the plant thoroughly with water. New roots started again. It is not dying but the top branches look dry all the time. It has new leaves coming through but they did not last very long and soon dried out. What is the problem with it? How do I make it better? How should I care for it generally? I don’t want it to die, as it belonged to my late father and it reminds me of him. Any advice you can offer will be appreciated.

They may have root rot and be dying. This article will explain how to treat it:
https://www.gardeningknowhow.com/plant-problems/disease/treating-root-rot-gardening-tips-for-housplants.htm