Just to verify, this is your original circuit:
The issue is the 3V zener is trying to hold the input voltage to 3V which it is not capable of.
Consider a car where the driver is holding the gas pedal to the floor (similar to the input voltage) and they have the brakes on (similar to the zener diode).
The engine will overpower the brakes, and eventually the brakes fail (i.e. zener fails)
When i increase voltage ober 3V i see the led bee brighter and if i turn voltage high enough, the led is damage.
Question1: What input voltage is causing the LED to fail?
Question2: Is your goal simply to stop the LED from flashing bright when the power supply comes on? Or are you trying to keep the LED brightness constant.
Question3: What is the range of you expected input voltage?
I think you may need an active regulator instead of a zener.