Eliminate AC noise from DC supply?
Decouple the IC as said in the remarks above: 100 nF close to the IC across Vcc and GND. A 10uF or 100uF cap next to it will help too if the 12V power supply lines are long.   

Moreover make sure the 100 ohm resistor (connected to up) is close to the transistor and both are close to the 555. And most important, add a 100 ohm between Low and pin 2 of the 555. The resistor should be close to the 555 again.

It is most likely the wire to pin 2 of the 555 picks up noise and makes the 555 trigger incorrectly. Adding a resistor close to the 555 willl attenuate that noise. If that resistor is far away, noise can still couple into the line and triggger the 555 incorrectly because it won't 'see' the 100 ohm resistor.