I have used bungees for the past 12 years to attach things to motorbikes, usually things that stretch the bungee beyond it's reasonable limits and never had one snap or break on me.
With all things, check them regularly for signs of fatigue, wear and tear and.
If they're showing signs of rust, replace them.
If they are significantly less springy than they should be, replace them.
If that make a funny noise, replace them.
If you're unsure about their condition, replace them.
it's all common sense, very rarely indeed will something snap without warning. They are, I agree a potential hazard and should be treated appropriately as with knives, saws, big sticks, water and fire.