Change of suspension behaviour

[Paul-R]

My C5 used to alter its suspension height as I loaded up the rear of the car. Just recently it's stopped doing that and only pumps up after starting the engine.

A thought occurs to me that it may be because the battery needs replacing, the logic being that the ECU detects that the battery voltage is low and avoids stressing the battery until the alternator can supply what's needed.

Could this be possible? The battery is a bit iffy as it has given me some heart-stopping moments during the cold snap and I was looking to replace it before the next winter.