As I said before, the capacitor needs to be enormous for that to work.
What's the resistance of the relay coil?
Yes, the capacitor obviously has to be in parallel with the power supply otherwise the relay will turn off as soon as the power is disconnected.
Even if it's high resistance reed relay with a resistance of 1K you'll need a 22,000uF capacitor for it to hold for 20s and that's before the 555 timer's current draw is taken into account.
You could get rid of the 555 and add a trimmer resistor in parallel but it will be less reliable as the delay will depend on the power supply voltage and temperature.
What's the load current?
A typical read relay will have a maximum current rating of 500mA.