3-way switches don't have power
Electrical problems such as this, you're more than likely going to need an electrician..I will NEVER advise people to dig into wiring.

A bad sign:

You mentioned this circuit only works a couple times a year ? Oh boy, that is NOT good.

What it could be, and what a homeowner can do without digging into the wiring:

Post a person AT EACH SWITCH for ease of troubleshooting.
(person 1, person 2)
Person 1: Flip the switch, (only once) &amp; observe the light
What happens ? 
Does the light come on ?
If yes or no
Person 2: Flip the switch ( only once) &amp; observe the light
What happens ?
Does the light come on or turn off ?

Now that both switches are in the opposite positions of where you had them:

Person 1: Flip the switch... What happens ?
If the light comes on or doesn't come on:
Flip it again. Once again, if the light comes or doesn't come on...
Person 2: Flip the switch... What happens
Wether the lights come on or not, Flip the switch again.

All the above is doing is checking to see if one or more of the switches are bad or if they were possibly MISWIRED.

If you ever remember these working fine at one time, I can say with a good degree of certainty that it's a faulty switch or switches. And if it's only one that's bad, I'd still replace both due to age alone.

It's always best to get a electrician involved when you see all your breakers are on and you've got a intermittent problem.