Why many (resistor - LED)s connecting in parallel, current of each LED is not stable?
Simple: Because your power supply can't reliably deliver the current for the high number of LEDs.

The current through a single LTL-307EE is, according to the datasheet of that LED, 20 mA. Hence, 40 branches will draw a current of 0.8 A.

Note that the resistor you're using isn't really the optimal choice for maximum brightness, here – at 20 mA, it should drop 1V, but instead, it drops 20 mA * 100 Ohm = 2 V, so you end up with significantly less current – it's hard to say, because the I/V curve of a diode is nonlinear, but you're probably getting half as much brightness as you could. Try using 50 Ohm! (Hint: two parallel 100 Ohm resistors form one 50 Ohm resistor)

When you draw more current than what your supply can deliver, power supplies must drop their voltage – that's a physical necessity.