Don't worry too much that you might have let one get by without knowing for sure if it has sucked. I expect most of us have probably done that at one time.
Everybody has different practices when it comes to calving and all of us don't calve in barns or calving pastures. Night calving is the cow's job around my place. I might see a cow with a new calf from a distance the next morning and write it down in my book and then not see her close enough to tell if the calf has sucked for a few more days. I try to see them all, but sometimes sht happens.
To answer your question about how long they can live, I've had calves live six or seven days without sucking. By this time, I'm pretty sure you'd know it if that calf hasn't sucked. Calves that haven't sucked in a long time are pretty desperate. In my experience, they'll bawl a lot and will even come toward you if you get close. Also, a calf that old that hasn't sucked will be so gaunt that you'll almost be able to see through him.
Other than fill, the yellow crap is what I always look for. Unless I see a calf actually sucking and swallowing, or unless I see him really full, I don't feel sure about it without seeing the yellow crap. If you still can't tell when you get him caught, try smelling his breath. Stick a straw up his nose to make him cough and you should be able to smell milk if he's been sucking.
Some good advice here, so shake off the poor deliveries that came with some of it and try to realize that everybody is just trying to help. Luck.