Is there any reasons or specific condition to trigger this on/off?
The theory of operation is,
- At \$t=0\$ all transistors are off and capacitor is discharged.
- The 4.5 V battery and 470k resistor slowly applies a tiny current (\$\dfrac{4.5 V}{470k\Omega}=9.57\mu A\$) to the 9013 NPN transistor base by charging the capacitor. When the 9013 base reaches about 0.6 V, it has just enough current to "activate" and short its E-C pins. The capacitor has about 0.6V (in reverse) across it.
- The 9013 collector is now at battery negative potential, so pulls a large current* through the E-B junction of the 9012 PNP transistor. This also causes the 9012 to short its E-C pins, so full battery voltage is supplied to the LED and it illuminates. This current will be about \$\dfrac{4.5V-2V}{100Ω} = 25mA\$, so the LED will be very bright.
- The capacitor had (negative) 0.6 V across it, but now 4.5V is supplied from the right side 9012 - so the 9013 base is supplied 4.5-0.6 = 3.9V for an instant. This quickly depletes the capacitor, and the 9013 base is once again near 0.6 V. But this time, the LED is lit and *both transistors are dissipating current, so the battery voltage is lower than 4.5 V, so there isn't enough current supplied by the 470kΩ resistor to keep the 9013 conducting and it switches off. The cycle then repeats.
This circuit is not ideal in many aspects. First, it depends on the battery having a high-enough internal resistance that it's voltage will drop enough when "on" to allow the 9013 to "open" and the cycle to reset. Use a different type of battery (or a "fuller" or "emptier" battery) and it won't blink at all.
Second, when the 9013 turns "on", this allows a large current to flow through 9012 E to B, then 9013 C to E. This is essentially a diode junction-drop (in the 9012 E to B) so 0.8 V or so. While on, this "diode" is directly across the battery - so Amperes could flow given big batteries. Such current needs limiting, likely by adding a resistor. But adding said resistor will influence circuit operation...
So to answer your question, the design of the circuit is dependent on the exact transistors used, exact voltage and internal resistance of the batteries, temperature, sunlight, amount of wind, phase of the moon, etc. There is no single "fix" that will make this design work correctly 100% of the time for 100% of conditions. There is a closely related circuit though, the astable multivibrator which is much more robust. Such a multivibrator, combined with a lamp and two big 6V batteries, powered the blinking amber road barrels in the US for decades. Their operation is largely unaffected by environmental conditions.