USB 100mA unit load average/rms or instantaneous
Since the other end has an over current protection circuit, I'll bet it's a hard and fast 100mA limit. If you have a pulsed current, you'll have to smooth out the power somehow otherwise you hit the limit (even if it is briefly) and your power will shut off. I'm not sure if there is a time limit in the spec, I'm not even going to check because its easy to overcome this problem.

The equation for sizing a cap to make sure you can ride this bump is:

$$C=I\frac{\Delta T}{\Delta V}$$
Where I is the current, t is the time of the event and V is the difference in voltage away from the rail. 

So if you can only dip down to 4.9V then the \$ \Delta V\$ would be 0.1V.
and the cap would be 

$$ C = 200mA \frac{2uS}{0.1V} = 4uF $$

So a 10uF cap would prevent a 0.05V drop and probably be sufficient.  You may ave to put a series inductor to prevent inrush current when the device is plugged in from the capacitors. This would also help filter spikes.