your drain from the kitchen goes down from the wall to a horizontal pipe for a long distance before it is connected to the main drain.
This section of pipe (probable a 1 1/2 inch or a 2 inch) does not have sufficient slope to facilate the flow of water. Water flows too slowly, and the grease accumulates.
The clog is caused by hardened grease. You need to run the snake multiple of times, each time retrieve a small portion of the clog until it's all clear.
There is no easy way to eliminate the problem permanently unless you change the slope of the drain. Otherwise you can change the way you do you dishes, avoid putting grease into the drain.
