Oscar de la Renta is fighting back against rumors that he is ill and may give up the reins of his company. Fashion insiders were abuzz about de la Renta’s failing health during New York Fashion Week last month, after the designer, 78, recovered from hip-replacement surgery. Though he was well enough to walk the stage at the end of his show, insiders say that since then, “Oscar is in the office taking meetings, but is weaker and takes naps to rest. There’s speculation that staff and designers have recently been hired to prepare for a possible future with Oscar taking a lesser role.” But a spokesman for de la Renta, a favorite of Sarah Jessica Parker and Demi Moore, said his health is solid and he has no plans to retire. “Oscar happily is enjoying excellent health. He’s putting in a full work day every day. Any new hires have nothing to do with the design process, and there is no plan whatsoever to even think of replacing him as the creative head.”