In late March, Angelica Donati, an Italian infrastructure and real-estate entrepreneur, started calling local banks seeking a loan to shore up her business after it was shut during Rome’s battle to contain the coronavirus.

Ms. Donati was expecting the loan to come fast under a government-guarantee plan. This backstop in theory lowered the risk for banks and sped the approval process. Of six banks she dealt with, two stopped taking her calls. She is still in talks with the others about what paperwork she needs. She was told the process may take two months from the application date.