I'm confused. In the first post, you talk about powering the circuit with either a 12V DC adapter, or three AA cells (4.5V). Why has the discussion turned to 9V batteries?
The three AA batteries may be too low to drive the circuit after the voltage drops a small amount. The amplifier can take more voltage, so my recommendation would be to add a fourth AA battery to your circuit. The AA batteries should drive the circuit, and will last much longer than any 9V you could get.
It also sounds like you are using poor quality, used, or old AA batteries. Use either new alkalines or some flavor of rechargeable. I recommend NiMH. They come in capacities up to 2700mAh nowadays.