The 24-year-old's father, Mitch, drove her to the hospital in his taxi after she fainted and nearly fell down a flight of stairs. Though she recovered quickly, her spokesman said she was examined as a precaution. Originally, she was expected to be released today.
"Doctors want to get to the bottom of it before releasing her," Winehouse's London spokesman told PEOPLE. "There will be further tests and they will keep her under observation. She seems to be fine ... but they are taking their time to be sure."
Meanwhile, in a new interview, Mitch admitted that his daughter's two-week rehab stint in January was a failure.
"She didn't want to get clean then, but she's talking about it now," he told the U.K.'s Closer magazine. "She's nowhere near as bad as she was [then]. A nurse visits twice a day and we're kept well informed about how she's doing. She's making progress."
Mitch, 57, said the singer wants kids with her jailed husband Blake Fielder-Civil – and will wait for him.
"Amy understands Blake might have to do a long time in prison – she's not stupid," he told the magazine. "But she'll stand by him and he'll stand by her." (Earlier this month, Fielder-Civil pleaded guilty to charges of assault and attempting to pervert the course of justice.)
Mitch added: "She wants kids and knows she can't be taking drugs, or the baby would be addicted – she wouldn't do that."