How long can bird eggs stay alone?

That depends on the egg and the bird as well as the climate where nesting occurs. There are a lot of variables. Lots of them. With some 10,000 bird species, no single answer will begin to cover it. Let's look at just a few birds for examples. In general, many eggs need to be incubated, kept warm by one of the parents. If one of them isn't on (or monitoring) the nest, the egg can die in hours or even minutes. In the case of the Emperor penguin, the egg must be kept on top of the bird's feet to be covered and kept warm. If the egg rolls off the feet of the parent, that parent has almost no chance of being able to get the egg back up on the top of its feet before the cold kills the embryo. It takes only minutes in the severe cold to kill the egg. A group called the megapode birds, or mound birds (or, perhaps, incubator birds), builds a large (4+ meters) mound of material and uses this to cover the eggs and keep them warm. By adding or removing material, the temperature is regulated. In good weather, the eggs may survive without care for weeks if the weather cooperates. The Egyptian plover, or crocodile bird, buries its eggs in the sand, and they stay warm there. They can be cooled by the adults by the trick of their soaking their breasts with water and pressing themselves down on the top of the buried eggs to transfer this cool water onto the sand. These eggs might survive for several days without care if the weather helps. These are just some of the ways birds care for their eggs. Mortality of the eggs will vary as widely as the type of nest and the care the bird gives the eggs as well as the weather at the nesting site. Remember that there are some 10,000 birds inhabiting almost all corners of the world. There are a huge number of variables.