I'm so very sorry for your loss, this is never easy no matter the cause. I know it probably won't help you much right now, but I highly doubt that your sleeping-schedule had anything at all to do with his death, especially if you were covering his cage at night. They can sleep through just about anything as long as they're covered, and many people keep their bird's cages in their living room or TV room, and at night they cover their cages while they are still awake and watching TV, talking, etc. And their birds sleep just fine. So I don't think that was the cause of your little Budgie's death.
Budgies are extremely prone to mite infestations, and their are a few types of mites that are very aggressive. Usually what happens is the as the mites rapidly multiply on the bird, there are more and more and more of them feeding on the bird's blood, just like a mosquito does when it lands on you. And unfortunately a tiny little bird like a Budgie cannot stand to lose much blood at all before they become severe anemic and finally die due to the loss of blood cells. So I'm certain that's what caused his death, and it doesn't take long at all for that to happen once you see the first signs/symptoms of them having mites, it usually happens within a day or two without treatment by a Vet. The mite remedies that you can buy in pet shops and grocery stores do not work at all, so the only thing you can do to get rid of the mites is to take them to an Avian Vet or Exotics Vet who can give them a single injection of an anti-parasitic medication called Ivermectin. With a bird as small as a Budgie, it's extremely important that they get the injection of Ivermectin quickly after seeing the mites, but also that you have a Veterinarian give them the injection instead of trying to put topical Ivermectin drops on them or giving them oral Ivermectin by mouth that you can buy at some pet shops and Tractor Supply stores. The reason the Veterinarians give Budgies and other small birds a single injection of the Ivermectin instead of giving it to them by-mouth or by putting it on their skin is because Ivermectin is a poison, and if you put it on a small bird's skin or give it to them by mouth, you almost always give them too much, especially if you put it on their skin, because they'll just keep absorbing it all up through their skin and they end-up getting far too much of it, and it poisons the bird. So a single injection of Ivermectin in a very carefully measured dose by a Vet is the only safe way to get rid of any type of mite or other parasite infection/infestation...And like I said, it happens so quickly after you see the first sign of them having the mites that if you don't get them to an Avian or Exotics Vet for the Ivermectin injetion almost immediately, it's just too late to help them and they die of the blood loss from the mites...
So it's not at all your fault, you were planning on taking him to the Vet, he was just too small a bird to be able to survive for very long with the mites. Please don't blame yourself, I know it's hard not to, but it really wasn't your fault, this happens to many, many Budgie owners, and it certainly isn't their fault. And now you know what needs to be done as soon as you see the first sign of a bird having mites, and how quickly it has to be done...
Make sure that you completely and totally disinfect his cage and everything inside and outside of it, the complete cage, the perches, all of his toys, the food and water dishes, and anything else in your home that your Budgie had any contact with, because a lot of mites can live on people and other pets such as dogs, cats, rodents, reptiles, etc. So you don't want you or any other people in your home or any other pets you have to get them. And be sure to soak the cage and everything in it in hot water and something like Bleach or another disinfectant like F10SC and rinse them well...
