did you by any chance also take anthropomorphic measurements? Did she complain to you of her clothes fitting differently? Those can be just as accurate indicators of change.
Such a body fat increase in the absence of weight gain is all but impossible. Even though her exercise routine is moderate, it should be sufficient to maintain her muscle mass. You mention that she is very consistent in her food intake. Bio-electrical impedance is also sensitive to hydration levels.
Regardless of the outcome of this question, I would not measure body composition once a month on a client like her. Given her moderate exercising, it is not likely to change significantly and may just make her feel worse.