You are too far away for the system to work properly. The chunks are not loaded.
As you walk around, you are loading and unloading chunks at a specific distance from yourself. In single player, the view distance determines that specific distance. Normal view distance is 8 chunks.
From the wiki:
The exact number of generated chunks varies in single player mode, depending on view distance and movement.
Chunks within the set range may have activity (mobs spawning, trees growing, water flowing, dropped items disappearing etc.), while chunks outside of this range are inactive, and are stored on the disk (this 'store until needed' memory management is commonly used with procedurally-generated terrain so that the players' computers don't have to track and update hundreds of plants and mobs simultaneously).
600 blocks is equal to 37.5 chunks which is above the view distance maximum. The train cart stops functioning once it reaches these unloaded chunks. Then as you walk down the track you are loading those chunks so the train cart goes back to functioning the way you expect it to.
One possible solution is to use a chunk loader design which purposefully prevents the out of range chunks from unloading. Here is an answer to another question with a couple of designs to do that.