I am personally aware of one case (my son) who recovered from Covid in December 2020, and was re-infected this month (Jan. 2022). He is not vaccinated, so it can happen. Both cases were extremely mild, no fever only loss of taste and smell along with congestion.
This is not scientific, but true. About a year ago a friend of mine had some slight symptoms and went for a free test which showed positive. A few days later he was fine. This Christmas, the same person became sick with mild symptoms, took a home test which showed positive. Several days later he recovered and is fine. Note that he is not and will not get vaccinated.