First let's zoom out a little on the schematic:
Grand Prix Delay relay (resized).jpg
The 1.0 uF capacitor you show above, in parallel with the Bridge Rectifier, is a smoothing capacitor that reduces the ripple in the DC voltage the rectifier creates from AC. This shows how the AC from the transformer gets rectified by the bridge, and then smoothed by the capacitor.
Rectifier (resized).png
Note that rectified and smoothed voltage isn't the same as DC voltage, but it's close enough. DC voltage generated from a battery for example has no ripple in it but is just a constant voltage.

The Delay relay coil in the upper left of the schematic has another capacitor (300 uF) in parallel with it. It delays the activation of the Delay relay after either of the switches on the Spinner relays closes.

Without the capacitor there, closing the L or R Spinner relay switch will instantly apply the smoothed, rectified (almost but not quite DC) voltage to the Delay relay coil which would activate it almost instantly, just like the jet bumpers just below it in the schematic. With the capacitor in place the behavior changes when the switch closes.

Capacitors can't change their voltage instantly and must instead be charged relatively slowly. So when a Spinner relay switch closes the voltage across the capacitor is initially zero, as is the current through the Delay relay coil. The voltage across the capacitor rises relatively slowly as the capacitor charges up, and the current through the Delay relay coil also rises slowly. Eventually the voltage across the capacitor rises high enough, and the current through the Delay relay coil is high enough to activate the Delay relay.

If your delay is getting longer you might try cleaning the two switches that drive the Delay relay coil. If they're dirty, that would increase the resistance of the switches and decrease the amount of current they could supply to charge the capacitor. That would make charging the capacitor take longer.

It's also possible that the capacitor has developed an internal short which would also make it harder (or take longer) to charge up.

/Mark

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