Such capacitors will draw very high peak current during switch on, and this may damage connectors and switches.
You can add an extra series resistor to limit this the input surge current.
For example, a 10 Ohm resistor will limit the peak current to 1.2A, which is probably a safe surge current for the 1n4148.
If your arduino draws a constant current of 50mA, then this will also cause a steady voltage drop of 500mV though, so this resistor is a compromise.
The power suplies of the arduino's have always been overly symplistic, which is quite sad unfortunately.
If you replace the lineair voltage regulator with a small SMPS module, then you can more then double the time that your capacitors can power the arduino board.
The ATMEGA328 works with voltages down to 2V (Some versions 1.8V I think) and it draws less current at lower voltages. So if you reduce the output voltage of your SMPS module, then you can again increase the time that you can buffer from your capacitors.
And of course other factors that influence the current consumption of your arduino pcb.
The simplest is to make as much use of sleep modes as possible. With this you can reduce the current consumption to (much) less then a mA. If your arduino has an always-on-led then removing that will also contribute to the buffer time, and all other connected circuitry will also influence it.