The most popular theory I've come across time and again regarding Sirius's death is that Bellatrix's second curse -- which is not identified as Avada Kedavra, as you say -- knocked Sirius off balance, causing him to fall through the veiled archway (the veil). The veil is a one-way ticket; it cannot be entered and then exited. When a person goes through the veil it means they have died and it is permanent.
‘Come on, you can do better than that!’ he yelled, his voice echoing around the cavernous room. The second jet of light hit him squarely on the chest.
The laughter had not quite died from his face, but his eyes widened in shock.
It seemed to take Sirius an age to fall: his body curved in a graceful arc as he sank backwards through the ragged veil hanging from the arch.
Harry saw the look of mingled fear and surprise on his godfather’s wasted, once-handsome face as he fell through the ancient doorway and disappeared behind the veil, which fluttered for a moment as though in a high wind, then fell back into place.
Harry heard Bellatrix Lestrange’s triumphant scream, but knew it meant nothing – Sirius had only just fallen through the archway, he would reappear from the other side any second ....
But Sirius did not reappear.
Order of the Phoenix - Pages 710-711 - British Hardcover - Adult Edition
Here's an explanation of the veil from the Harry Potter Wiki:
The Veil is the barrier between the land of the living and the land of the dead. One cannot travel freely between the two worlds, as it is a one-way trip. Inexperienced wizards know nothing about it, but the much more experienced wizards may have heard about it, and the Unspeakables who work in the Department of Mysteries have likely studied it closely.
A physical manifestation of the barrier (the veil) was somehow kept in the Ministry of Magic's Department of Mysteries; in the Death Chamber, a room large and echoing, dimly lit and rectangular, and kept in the centre of a raised stone dais in a sunken, great stone pit some twenty feet deep, with benches running all around the room and descending in steep steps like an amphitheatre (or like the Wizengamot Courtroom 10) and surrounded by a cold air and complete stillness.
Though the living could have the strangest feeling that there was someone standing right behind the Veil on the otherside of the archway, their words are inaudible except for "faint whispering and murmuring noises" coming from the other side of the Veil. When the living person attempts communication themselves, the dead try harder and their whispering and murmuring becomes louder. If those who hear the whispering stare at the archway long enough, they shortly become entranced and mesmerised by it, believing it had a kind of beauty about (old though it was), unknowingly walking towards it, intrigued by the gently rippling Veil, and feeling a very strong inclination to climb up on the dais and walk through it.
However, this would prove fatal, as passing through the Veil would cause instant death.
Hope this helps to answer your question :)