Series voltage reference unstable with a series resistor
If we disregard the voltage regulator, the two 1k resistors form a resistor ladder that divides the input voltage in half.  

The voltage regulator can only add impedance.  That means its output voltage can never be more than 50% of input voltage, and will in practice be less.  If your voltage supply dips below 10V, the output must dip below 5V.  

You are trying to dampen that with capacitors, but all that can do is slow this down a bit. If a &lt;10v state exists for any significant time, the regulator output must brown out.