A schematic would help but if I understand what you are doing, the 100V is dropped by the resistor before it reaches the LM317 and when you increase the load on it, the voltage drops.
This suggests the extra current through the resistor is dropping enough voltage that the LM317 no longer has enough at it's input pin to maintain it's 14V output.
Firstly, please be aware that although a resistor dropper will work in that circuit, if the load is removed or becomes too small, the voltage dropped across the resistor will be less and you risk the LM317 maximum input voltage being exceeded.
With that kind of circuit, the only way to allow more load is to drop the resistor value. A better method would be to use a small switch mode supply that can run on a high voltage input but still regulate 14V out, that will allow the load variation without the voltage changing but the circuitry would be a little more complicated.
Brian.