Of course, the peel was brown. If your banana ripens on the counter for a day or two and then remains in good condition after a week of refrigeration, the total time from purchase to spoilage would be not just 7 days but a whopping 9! So your problem is solved.I think bananas taste best when they're cold.) A reader's response to the lifehacker.com article says bananas will keep for up to 2 weeks wrapped in newspaper and refrigerated. My wrapped banana certainly wouldn't have survived a second week. My unwrapped refrigerated banana did not hold up as well as the wrapped one.