exactly this happened on my last cav, it was p**sing down seriously hard and the indicators just stopped. the light on the dash stayed on, but the indicators stayed off (so couldn't even flash them manually). hazards were fine though.
i pulled the relay and couldn't see anything wrong, but when i put it back everything was ok. i think it was down to the damp.
i reckon it is your flasher unit, like johann says, put the hazards on and locate the unit. get it out and give it a clean. if it's still no good, get a new one. they're not expensive (especially from a scrappie!)
The flasher unit on my Nova was on its way out for about 3 months. It used to stop every now and then and I just used to smack the relay panell. Relays are too hard to change on a Nova, you have to slide the fuse panel out to get at the back of it.
But I always say " You can't under estimate the ability of a good kick to fix things.
It could be the hazard switch itself. Just fixed mine, exactly the same problem as you. The hazard switch was shorting out, try gently wiggling/pressing the hazrd switch while the indicators are on to see if it starts working.
As the hazard lights are working, it won`t be the relay.
If the hazard switch is out of the dash, the indicators will not work as the electrical circuit for the indicators goes through the hazard switch so if the connections inside the hazard switch are worn, you get the problem you describe.