Getting Push Button Logic To Stick?
You'll need to store whether the button has been pressed.

bool buttonActivated = false;

...

void loop(){

  buttonState = digitalRead(buttonPin); //Read push button logic.
  if (buttonState == 1 ) {
    buttonActivated = true;
  }

  if( buttonActivated ) {
    printAccel(); //print sensor data
  }

}


to deactivate, use:

buttonActivated = false;