Almost certainly it IS going off but turning on again straight away. The code does not visually blink the LED, if RA3 is low it turns it on, waits 10 seconds, turns it off then turns it back on again. It probably blinked off so fast you didn't notice it.
I suspect what you want to do is make it turn on for 10 seconds, turn off then wait until the switch is pressed again. If you want to do that, you need to add a pull-up resistor (~10K) between RA3 and VDD so it doesn't immediately re-enter the loop.
If you want it flash continously 10s on, 10s off when RA3 is low, add another delay after "RC0 = 0;" so it has timed on AND timed off periods in the loop.
Brian.