Battery light stays on, alternator tested good

Hi, the battery light on my vehicle has been coming on frequently, and I lost all electrical power a week ago. I was able to get it to a repair shop, and they checked out the electrical system. Everything checked out fine, and they were reluctant to recommend a new alternator. They drove and tested it every day for a few days and everything ran fine. I have driven it since, and the battery light stays on constantly now, but now other issues. Any ideas where I should look next to resolve the issue?