My Snap Type is set to Events and Cursor. So the Range is not snapping to the Grid. But thanks for the idea.
Actually, I’ve figured out the cause of the problem: I’m in the habit of including the marker track whenever I select a range, so that the markers will keep their position relative to the audio clips when I Cut Time. But including the marker track in the range interferes with Snap to Zero Crossing. If instead I drag my mouse only on the audio clip, without including the marker track, then Snap to Zero Crossing functions correctly.
Thanks for the suggestions.