The darkest day in Matt White’s life arrived in June 2004, when his family-run Virginia advertising firm lost the Amtrak account and more than half of its revenue. “My heart went through my throat,” said the chairman of White64, the Tysons-based firm his “Mad Men” father founded in — no surprise given the firm’s name — 1964. Revenue dropped from $9 million annually to around $4 million. White64 laid off a third of its 60 employees. Executive salaries were slashed in half. Travel, entertainment, you name it . . . cut. Losing Amtrak also struck at the firm’s prestige, forcing White to get scrappy. After the Amtrak debacle, which had been the firm’s mainstay client for 25 years, White’s team remade itself — and has been remaking itself ever since. The firm is a case study in small-business survival and how small companies remake themselves or die.