NEW YORK – To the ranks of New Coke and the Edsel, we can now add Qwikster.

Less than a month after announcing a plan to separate its DVD-by-mail and Internet streaming services, Netflix reversed course Monday and said it would keep the two services on a single website.

Customers had complained loudly that the plan would have made it more difficult to watch movies.

Investors hated it. In the end, the company backed down.

But Netflix’s turbulent relationship with subscribers over the last three months raises questions about how it’s being managed during the transition from delivering movies on disc to sending them over the Internet.

Until recently, CEO Reed Hastings had always seemed to possess an uncanny touch. He was the David who crushed goliath Blockbuster and a visionary who foresaw the death of the DVD.

He was also a beloved leader who lavished his employees with above-market paychecks and unlimited time off.

When Netflix employees were asked to describe Hastings, they often pointed to the George Clooney character in Ocean’s 11.

But that cool, smooth operator seems to have vanished. Six months ago, Hastings and Netflix could do no wrong.

Today, he and the company are fodder for “Saturday Night Live” skits and targets of venom on social-networking sites.

Netflix’s about-face initially pleased Wall Street. The stock rose as much as 10 percent in the first minutes of trading. But enthusiasm waned in the afternoon, and Netflix ended the day down 5 percent.

Analysts praised Hastings’ attempt at a mea culpa, but the series of missteps has stirred doubts about his leadership at a time when the company faces wrenching industry change and ferocious competition.

“They’re making decisions rashly and also potentially out of desperation,” said Tony Wible, an analyst at Janney Capital Markets.