How long can baby birds live without food?

A baby robin fell out of one of our birdhouses yesterday, and I put it back inside. When I came home from work today it was on the ground again and I thought it was dead. Unfortunately it wasn't dead, which sounds mean but it must have been suffering all day and flies were leaving maggots all over it. I am still so sad and I held it until it ped on as peacefully as possible. My question, though, applies to the other baby I can hear chirping inside the birdhouse. I have never seen an adult bird enter or leave the house, though I don't watch the birdhouse all day long. If the mother bird is gone, then would that other baby still be alive? Or should I hurry to contact a local wildlife preserver? If there's no way that bird could be alive unless its mother is still feeding it then I don't want to steal it out of its nest.