Initially, aides had said the 88-year-old 41st president would be released from the hospital over the weekend. But he has a "nagging cough" and "we don't have any idea when he'll be released," said Methodist Hospital spokesman George Kovacik.
"They're not in any hurry, so they're just keeping him here, but there's really no change in his condition," Kovacik said. "He's stable and he's still here."
Bush has been in and out of the hospital for treatment of the cough since last month. The former president also has a form of Parkinson's disease that forces him to use a wheelchair or motorized scooter.
The ex-president and his wife, Barbara, live in Houston during the winter, and spend their summers in a home in Kennebunkport, Maine.
Bush's condition has improved in recent days, his spokesman in Houston, Jim McGrath, said, and he has been receiving visitors. While he has not been diagnosed with pneumonia, which can be dangerous in elderly people, and the cough is not life-threatening, the doctors and Bush himself prefer to wait until the cough goes away before sending him home.
"I was with him yesterday. He had a great day yesterday. He had a good night's sleep the night before, importantly, and his breathing was so much better. But he still has this cough, and when he coughs, it hurts," McGrath said. "The doctors don't really want to let him go until he's 100 percent."
Bush's wife, Barbara, has been by his side nearly nonstop, McGrath said. Previously, ex-President George W. Bush visited.
More recently, his son, Neil Bush, and his wife, Maria, who live in Houston, have been frequent visitors, along with their son, Bush's grandson, Pierce Bush, he added. On Sunday, former U.S. Secretary of State James Baker and his wife, Susan, also stopped by.
The highlight of the day, though, was the Houston Texans' 24-10 victory over the Tennessee Titans, a win that secured the Texans a spot in the NFL playoffs. Just a few weeks ago, Bush was spotted at a Texans' game.
"He was keeping track of when kickoff was and we were following the game there for a little bit," McGrath said.
In general, McGrath said, the former president's spirits are good.
"He's joking with the doctors and the nurses so he's not nearly in the same level of discomfort he was in just a few days ago," McGrath said.
Still, since he was released previously and then readmitted because the cough did not go away, there is a sense he should stay put until the cough disappears entirely, he added.
"A little bit is an abundance of caution, but a lot of it has to do with he still has the cough," McGrath said.
The former president was a naval aviator in World War II — at one point the youngest in the Navy — and was shot down over the Pacific. He achieved notoriety in retirement for skydiving on at least three of his birthdays since leaving the White House in 1992.
Plushnick-Masti can be followed on Twitter at https://twitter.com/RamitMastiAP
Copyright 2012 The Associated Press.