The microcontroller running at low speed will use less power than the 555 circuit, and that's what I'd probably use. Wake up, set the clock to the lowest speed you can, and sample the voltage a few times. Obviously a micro with a flexible clock would be good.
Alternatively, you may be able to make use of a peak detector to capture the amplitude. Combining that with a steep (high R, high C) RC lowpass filter will delay and average it, and you might be able to pull off the entire amplitude detection and averaging with a diode, two capacitors and two resistors. This may be desirable depending on what the signals look like and how versatile the MCU is.