what is the value of the capacitor you used? the capacitor in the breadboard picture looks like an electrolytic cap which typically have higher values than the 100nF specified in the schematic.
i didn't check the values specified in the schematic but assuming they are appropriate for the signal the hobby servo needs i think the circuit should work.
other suggestions
- double check all your wiring
- replace the 555 timer IC (ensure it is installed in the correct orientation)
- check the voltages at different points in your circuit and make sure they are what you expect
- (if you have access to an oscilloscope) check the output signal and capacitor voltage
