Hold-up time calculation with high capacity MLCCs
I think that the hold time for the MLCC can be calculated numerically as in the following example. The total charge in a linear capacitor Q is C times V. But MLCC is not a linear capacitor and therefore Q=f(V) (some function that we will assume known now). 

At time 0, let be V=5V. At this voltage Q0=f(5)=240 uC.

After some unknown small time step, the voltage dropped to 4.9 V. The charge in the capacitor is now Q1=f(4.9)=237.65 uC.  (for example).

Assuming a constant current sink I of 10 mA and remembering that I·(delta time)=delta Q. We can calculate delta time=(240-237.65 uC)/(10 mA)=0.235 ms. The first time step took 0.235 ms.

After the following time step, the voltage dropped to 4.8 V. The new charge will be Q2=f(4.8)=235.2 uC. This time step is then (237.65-235.2)/10 mA=0.245 ms.

If this is continued until the voltage arrived to the minimum allowable voltage for your circuit, you only need to add all the time steps to get the hold time. 

I chose voltage steps of 0.1 V, but values smaller or bigger can be chosen to get more or less accuracy in the final result. The problem remains to find function f(V).

The capacitance values from the "Capacitance vs DC Bias" graph in the datasheet gives the the relationship between Delta_Q and Delta_V at every DC bias voltage; i.e. it gives the capacitance seen by a small signal.

I think that a good approximation of f(V) could be obtained doing Integral(from 0 to V, of C(V')·dV'). Where C(V') is read from the "Capacitance vs DC Bias" graph.

Finally there is a FAQ from Murata http://www.murata.com/en-global/support/faqs/products/capacitor/mlcc/char/… where the physics behind the capacitance change are explained: 


  Without a DC voltage, spontaneous polarization can happen freely. However, when a DC voltage is externally applied, spontaneous polarization is tied to the direction of the electric field in the dielectric, and independent reversal of spontaneous polarization is inhibited. As a result, the capacitance becomes lower than before applying the bias.


This explanation would also apply to decreasing DC voltages. If DC voltage slowly decreases (during capacitor discharge) the polarization won't be tied to a particular direction and then the capacitance will increase.

The calculation of the hold-up time, using this method, can be done rather easily with Excel. I attach a worksheet with real datasheet data for a given 47 uF MLCC capacitor and the necessary calculations:
Hold-up time comparison betwween given 47 uF MLCC capacitor and a 40 uF linear one