PIC on 3 volts power
No. The PIC16F628A only works down to 3V, according to the datasheet. The LF version works down to 2V. Even with brand new AA batteries, the voltage will quickly drop below 3V, and can cause issues. 

Solutions. Use 3x AA for 4.5V nominal, or use a boost converter to bring up 1x AA or 2xAA to a stable 3~5V.