This is a favourite at conventions and meet-the-author events. I suspect the answer is that none of the authors really know. Some turn all prickly and prima-donna-ish at being asked such a question; some struggle to respond honestly. But they all give different answers.
For me, I'm a bit like one of those huge Bluewhales that swim with mouths perpetually open, sieving the oceans for tiny plankton. Without consciously trying some little part of my mind stays receptive while swimming along through life; and without deliberately selecting, I sieve the plankton of inspiration here and there, from experience, newspapers, conversations I've had or overheard (not intentionally, of course!). These are digested in the belly of imagination and eventually emerge as an IDEA. This IDEA takes me by surprise. Often I tell myself, 'Hell, I can't make a story out of that.' But the IDEA doesn't go away. And before long it grows into a story more or less of its own accord.
While I certainly aren't one for nicking anyone else's ideas there are some films, programmes, books and stories that have embedded themselves so deeply into my psyche I've had to go and wirte something in that general subject area. For some horror writers it's the vampire, or the haunted house. For me it has to be the disaster or apocalypse story; those that tell what happen when a band of survivors must rebuild after the collapse of civilisation.
One of the earliest of these to root itself deeply into me was On The Beach. I saw the film serialised on children's TV (strange programming!) over thirty years ago. God, how that scared me. It told of a vast nuclear war that killed off the population of the Northern hemisphere. Australia is largely untouched and that's where the story takes place. I watched in horrified fascination as the story unravelled, and began to understand that the characters were doomed because radioactive dust was drifting toward them. That fuelled many a nightmare.
Later I was enthralled by Terry Nation's 1975-77 drama series Survivors. This time a small group of Brits survive a new plague. Survivors was a ground-breaking series for the BBC as it was the first to be shot entirely on video and entirely on location (certainly the vast bulk of episodes anyway). The videos are now being released by Sovereign Multi-Media and are well worth checking out. There are also a couple of Survivors-related websites: survivor@globalnet.co.uk and http://freespace.virgin.net/christopher.barker/survivors.html
As for novels I had some rich pickings. For post-apocalypse stories my favourites are John Wyndham's Day Of The Triffids and The Kraken Wakes, and the fiendishly subversive John Christopher stories "A Wrinkle In The Skin", "The Death Of Grass" and "The World In Winter". I'd also tag the Christopher novel Sweeney's Island to this list; although not a post-apocalypse story as such its more of a Robinson Crusoe tale of a group of people ship-wrecked on a tropical island, still it touches on survivor themes. Most Christopher novels were retitled for the American market, so best read the blurbs if hunting for them.
Needless to say, I couldn't leave the survivors theme alone and have explored it twice; first in Blood Crazy and then in King Blood. I keep telling myself, 'That's it. No more post-apocalypse stories.' But whatever lies in the under-belly of my brain that supplies the ideas is whispering again. And I know for a fact that before long there will be a story where men, women and children are stripped of the protective cocoon of society, and will have to pit their wits against the environment in order to survive for just another day.