Peak detector circuit operation
But when I reduce the voltage on the input, the capacitor voltage also reduces, but it cannot discharge since there is no path. So how does it reduce its voltage?


It is not clear from your question whether you are observing this on a test setup or in a simulation. If you are using a multimeter with an imput impedance of 10 MΩ across a 0.1 µF capacitor then the discharge time can be calculated by \$ \tau = {RC} = {0.1 \mu \times 10M} = 1 \;s \$. In 1 s the voltage will have discharged by 63%, in 3 s it will have decreased by 95% and in 5 s it will have discharged by 99%.