The simple answer is that a writer can't ever stop looking for interesting things. I have a file of newspaper articles that caught my attention. I have a journal of great lines from books I've read. Right now, however, I find the most potent source of inspiration to be in ideas not followed in the stories that I love.
Let me explain with an example from a favorite book by Robert Graves. In I, Claudius, the character Claudius spends most of his early adult life watching his grandmother, the Empress Livia, manipulate her way into sustained power through suggestion, blackmail, and even the poisoning of family members who oppose her wishes. Near the end of her life, Livia summons Claudius to dinner. He's not sure if he'll survive the meal, but he goes along. The meal contains the beautiful beating heart of the book, a drunken, brutal conversation between murderous grandmother and stuttering Claudius. She admits everything in those hours: who she murdered and how, how close Claudius came to winding up a victim himself for his snooping, and why she did it all (she says) for the security of the empire. He lets her live out the last few years of her life and does what she begged him to do for her.
What if Claudius acted on what he guessed long before he had the conversation with his grandmother? Could he have saved his brother or his cousins? What if he played politics the same way Livia did -- poisoning the poisoner? What if... What if...
It's an incredible scene in a very good book, but I read it and wish Claudius had done something else. In those bits of wishing lay the seeds of future stories I might choose to tell. It's the older stories, the beloved ones, that excite us to tell new stories. Why not take something of the old premise and refresh it, follow the story to an old fork and take a different decision path?
What if Hamlet killed Claudius in Act One just after the Ghost delivered his message? How would that tale go? A civil war between Gertrude's side and Hamlet's?
What if Nick Carraway refused to play intermediary to Gatsby and Daisy? What if Gatsby tried to get Daisy to leave New York, head to Paris or Rome with him? What if? What if?
Find a moment that makes you unhappy in a favorite work. What are the better choices? What could you do to create a new plot out of the circumstances? What new complications arise from the changed story?
Tell an old story, but make it new. Make it your sort of story, a twist on the original that only you could pull off the right way.