Relay Delay Off

Hi, I am not sure why you eant to set-up such a system. But what you are trying to do is power up the circuit through a secondary source after the primary power is actually turned off. Well bascailly the best way is to use a small coin cell. But if you just want to make the circuit stay live for 5 seconds then you can either use a powerful capacitor in parallel (like you have already done) or use super capacitor.

I am not sure where exactly you are connecting this diode in the circuit (providing a circuit diagram will help). but diodes noramally have a high coltage drop across it (0.2V) either you can try using a schottky diode instaed of a normal diode like 4001 or provide the circuit diagram here to acually check what the problem is 

Their purpose is to control an event based on time. The difference between relays and time delay relays is when the output contacts open & close: on a control relay, it happens when voltage is applied and removed from the coil; on time delay relays, the contacts can open or close before or after some time delay.

Time delay is defined as the controlled period between the functioning of two events. A Time delay relay is a combination of an
electromechanical output relay and a control circuit. The control circuit is comprised of solid state components and timing circuits that
control operation of the relay and timing range. Each function is explained in the table below. Time delay relays have a broad choice of timing ranges from less than one second to many days.There are many choices of timing adjustments from calibrated external knobs, DIP switches, thumbwheel switches, or recessed
potentiometer. The output contacts on the electromechanical output relay are direct wired to the output terminals. The contact load
ratings are specified for each specific type of time delay relay.