##Limit##
Yes there is a limit, minecarts will only go until the end of the chunk, but they will not stop. Minecarts only pause at the end of a chunk, and when the chunk is loaded it will keep the same momentum and will continue to move.
##Solutions##
**Mods**

 - [Railcraft][1]

**Vanilla**

 - [//forceload][2]
 - [Chunk Loader][3]

##Notes##
Minecarts will lose momentum once you log out. If it pauses at a chunk and you log out then go back into the game the minecart will be frozen. If you are on a server that will keep running once you log out then it will be fine.
  [1]: https://minecraft.curseforge.com/projects/railcraft
  [2]: https://minecraft.gamepedia.com/Commands/forceload
  [3]: https://gaming.stackexchange.com/questions/125290/can-i-use-a-hopper-loop-as-a-chunk-loader