Why don't multiple eclipses happen over the course of a few days?
The reason is because the moon moves much faster (in terms of angle per day) than the sun. In fact it moves on average 12.5 degrees per day, and all in the same direction.  Given that the sun is only about 0.5 degrees in diameter, it doesn't take long for the moon to overtake it, and once it's past  it doesn't go backwards.