The extreme stock-market gyrations in August exposed cracks that many critics had warned about in the booming business of exchange-traded funds—cracks that fund managers such as BlackRock Inc. are now acknowledging as they work to figure out what went wrong.

At issue is one of Wall Street's most popular products ever. Investors have poured hundreds of billions of dollars into ETFs over the past decade, drawn by low fees and the prospect of being able to buy or sell a mutual-fund-like product whenever they want like a stock. But trading records and conversations with investors show ETFs couldn't keep that promise when the Dow Jones Industrial Average dropped more than 1,000 points in the first minutes of trading on Aug. 24.