"gain error" of rectifier circuit
Every time Vin crosses zero, A1 output signal should perform step (immediate change) by twice D1 forward voltage, which is about 2*300 mV for BAT54.  

According to AD8602's datasheet, it's slew rate is 5 V/us, so time required for that step is about 0.1 us which is not so small relative to half of Vin period at 200 kHz (2.5 us). During this step feedback loop of A1 becomes open and when it closes, oscillations may occur. To prevent such unwanted behaviour C1 is used. It keeps feedback loop of A1 always closed for the cost of slowing down the transition. Also, during it's time the cirquit does not behave as an ideal rectifier. For example, it may output negative voltage. So, C1 value is crucial for behaviour at high frequencies. Also, I guess that frequencies such as 100 kHz are rather high for the selected op amp type.