What are the general characteristics of a faulty Arduino UNO board?
Any RTC that depends on an internal oscillator will drift with respect to time, the only question is how fast. As well as inherent drift, temperature changes, voltage changes and noise can affect the timekeeping. According to the chip datasheet:

A drift of 1 minute per day (700ppm) is much more than one would expect from a crystal by maybe 50 or 100x so maybe the issue is noise coupled from the Arduino reads and poor layout or circuit arrangement in your implementation or in the design of your module (presumably an inexpensive hobbyist-oriented product).
If the clock is running fast, this is most likely the issue. If it's running slow, then it may be something else.