Sounds like a gas pressure issue, make sure the gas lines are not bound or pinched.
The pilot light should not be off or too low, and should be carefully adjusted to have a low burn to ignite the main burners.
When the main burners are on and suddenly go out, it could be an indication of poor flow of either too much gas or too much air, because air is required for the flames to flaming. A quick through cleaning of the burners should do the trick.
Hope that helps
-SF