Sounds to me like you are getting false triggering of the 555s due to noise on the power supply. There are a few solutions I might offer, none better than the other.
- A large (1000 uF or so) electrolytic capacitor directly across the battery.
- A small value (100 ohms or so) resistor in series with each 555 power lead bypassed on the 555 end with a moderate (100 uF or so) electrolytic capacitor.
- A small power diode (1N400x or similar) in series and a capacitor as in suggestion #2. With this one, you might be able to get away with only a single diode and capacitor and all three 555 power leads tied together.
Jim