When LED shower heads stop lighting up, it’s typically due to mineral buildup, or the lights are simply broken.
The lights inside your LED shower head use a turbine for power. If there is mineral buildup inside the shower head, this turbine won’t be able to produce the energy required to power the lights. When your shower is clogged, you have to clean it.
If the LED lights are broken, there’s nothing you can do except buy a new showerhead. If your shower head is still in its warranty period, you might be able to have it replaced at no cost.