Why don't multiple eclipses happen over the course of a few days? From my understanding over the course of the seasons the moon and sun rise at varying locations. Though the day to day differences are no noticeable, to me at least. For instance, in the summer, the sun takes a longer path overhead as a result of the earths tilt towards the sun in the summer months -- in the winter, short paths. 

With the seemingly negligible difference in path lengths of the sun from day to day why then do solar eclipses only happen on a single day and not over the course of many days? It seems that if the moon and sun paths during the day were to intersect they should do it multiple days in a row as their path lengths across the sky during the day change.

I assume the answer to this lies particularly with the moons orbit around the earth and its shape/inclination. But I am far from my last astronomy courses and have lost all the jargon and knowledge needed to determine this.
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.