Space.com has an interesting article that discusses this very question. Basically, it postulates that everything will eventually go away, due to micrometeorite bombardment, etc. It has the following to say about the rate of deterioration:
From past studies of moon rocks collected by astronauts during the
Apollo missions, researchers have learned that the rocks erode at a
rate of about 0.04 inches [1.0 mm] every 1 million years.
Given that rate, how long would it take the footprints to disappear? I'm going to guess that the footprint is about an inch (25 mm) deep at it's tallest, and the detail is about a quarter inch (6 mm) (The tread). Given those numbers, it'll take about 6 million years before you won't easily be able to recognize it as a footprint, and about 25 million years before it's completely gone. This assumes that the area doesn't get struck by a particularly large meteor, which would accelerate the rate, and that nothing is done to protect the area in the mean time.
It's worth noting that the provided erosion rate is for rock. The dust might have a higher rate, as it does on Earth, but it likely won't be that much higher. This will be slightly complicated as well that there is a small dust storm that happens at the terminator of the moon. I strongly suspect that the footprints will be gone in a million years, if nothing is done to prevent it from happening.