Can a surface-mount ceramic capacitor fail partially and intermittently?
3 possible conditions I can think of that could cause psudo-random appearing intermittent issues. 


Temperature. Ambient and operational temperatures can cause dramatic changes in performance depending on the specific component specs and tolerances. 
Physical stress. Bending of the mounting surface can cause deformation and therefore changes in capacitance. They usually don't have much give in them before they crack and fail open/short, but a light flex or moderate pressure during operation can cause unpredictable results. 
Piezoelectric Effects. Certain electrical conditions can cause multilayer ceramic capacitors to vibrate, and any vibration can case them to generate a voltage back into the circuit. If your circuit only enters a state where it causes a piezoelectric vibration under certain conditions, or the usage conditions create random bumps and vibrations by the user, then you could have undesired and intermittent issues.