How does a split rail supply work and how to design one?
The actual problem is that you precision rectifier is measuring the negative cycle of your input waveform (which, by the simple fact that it seems to be somehow working must be an actual centered AC). During the positive cycle the opamp is saturated, not just by the presence of the diode but by the signal itself, this can be considered either a bug or a design feature in this case. By giving it a positive DC you have simply put it out of range.

You already have a split rail in your design. You created one for biasing node "A" at the input of the first opamp. You can do exactly the same thing for biasing the positive terminal of your super diode opamp, but this means that you will lose half your range as now the DC will determine your new minimum output value.

If, after you set your mid-supply bias, you AC-couple your super-diode it will work and behave as it should, but now the negative cycle of your input waveform defines the bias point of the op amp and keeps it saturated. This is what is known as a DC-recovery circuit. However, this bias point is the same as the rectified value.

The only thing missing, after AC-coupling, is to provide a discharge path for the output capacitor when the OP amp is saturated. You can do this by adding a resistor to ground in either the input or the output of the super diode.

But BTW: the way that AGC circuits normally work is by looking at the peak output of your amplified signal and trying to keep it constant. That is, setting the gain via a feedback algorithm not a feedforward one.