In 1958, worried that America was trailing the Russians in the great technology race, President Dwight Eisenhower signed into law a bill he believed would kick-start American innovation and put the U.S. back in the lead. The Small Business Investment Companies Act not only created a unique public-private partnership that reignited the country’s passion for innovation, it also spawned the modern venture capital industry, which would go on to bankroll entrepreneurs’ ability to turn their dreams into reality. Some of the most important U.S. corporate success stories — from tech titans Apple and Intel Corp. and biotech pioneers Amgen and Genentech to more recent e-commerce leaders Amazon.com and eBay and social media darlings Facebook and Twitter — were initially backed by venture capital.

But now, a half-century later, the venture capital industry is struggling. Profits are virtually nonexistent, and for the first time in...