The changes in people’s mental health have become one of the hot topics during the COVID-19 pandemic. Parents have been said to be among the most vulnerable groups in terms of the imposed anti-pandemic measures. The present paper analyzes the trends in mental health indicators in a sample of Slovak parents (N = 363) who participated in four waves of data collection over a year and a half of the COVID-19 pandemic. The mental health indicators were represented by general levels of depression and anxiety as well as COVID-related stress and anxiety. While there were only minor changes in depression and anxiety, the dynamic in COVID-related stress and especially anxiety was more noteworthy. Besides some exceptions, the results hold even after controlling for the socioeconomic situation. The gender differences in the mental health trends were found to be negligible. Overall, we observed no substantial deterioration in the mental health indicators across the four waves of the study.