LDR / photoresistor issue: resistance is constant in different light conditions
Don't know if this is the cause of LDR failure, but your circuit has a basic flaw: A +12v supply can cause damage to the ATmega328, when the photo-resistor's resistance is low enough to raise the Analog input pin above ATmega328's Vdd (+5v?). Too much current can flow.
The solution is to lower the +12v supply to no more than ATmega328's Vdd voltage. You may have to lower the threshold where you decide if the laser beam has been blocked, because with a lower supply, your circuit will be less sensitive.