ADC transient malfunction or ESD failure?
I think your problem is probably the reset circuit, since resetting the MCU restores operation. If the microcontroller is improperly reset at power-up there is no guarantee of proper operation and the exact effects may vary from unit to unit. 

The clamp Schottky diodes allow the op-amp to hold the power up and reducing the negative rail filter cap means that the op-amp output will likely hold the Vdd on the micro above the guaranteed reset zone longer than if the negative rail cap was larger. 



If you don't ensure the supply voltage drops below 700mV and rises faster than 50mV/second, the reset is not guaranteed. 

It is most reliable to use an external reset IC which guarantees a minimum reset pulse width of perhaps 200ms and properly handles all combinations of short and long interruptions of power or brownouts, but the internal BOR may well work for you if you enable it, particularly at 5V.  

As a quick fix, you can hang a resistor of maybe 1K across the Vdd to GND, which will discharge the power supply relatively quickly.