I have these in my kitchen in my new house and one strip seems to have “burned” out. Is this possible or is it just a faulty installation?

I'm not sure about these Good Earth strips, but I have Utilitechs that I bought from Lowes about 3 years ago. One set has dimmed to the point that it puts out almost no light. That said, I would answer that it is, in fact, possible that these things burn out over time.