Dear Oren,

I think your problem is caused because the high voltage spikes caused by your neon lamp starter. When the light "blinks" during turning on, the line is "contaminated" with high voltage, short duration spikes.
I think you should add a LC filter in all low-voltage external conections of your board and add some decoupling capacitors (maybe a EMI line filter may help). The neon lamp must be conected out of the line filter circuitry.I had a problem like yours with a safe lock project (solenoid).

Good luck.