Just over a year before Silicon Valley Bank’s collapse threatened a generation of technology startups and their backers, the Federal Reserve Bank of San Francisco appointed a more senior team of examiners to assess the firm. They started calling out problem after problem.

As the upgraded crew took over, it fired off a series of formal warnings to the bank’s leaders, pressing them to fix serious weaknesses in operations and technology, according to people with knowledge of the matter.

Then late last year they flagged a critical problem: The bank needed to improve how it tracked interest-rate risks, one of the people said, an issue at the heart of its abrupt downfall this month.