Also what game version are you using?
Autopilot has had some difficulty in DL that "should" "mostly" be fixed in later versions.
In particular there is a "path too long to calculate" error that can occur and be logged in your debug.err file. This is simply as it says and can be gotten around by scheduling autopilot over shorter distances.
There is also the problem that occurs over a save and reload where ships can simply "forget" they were on autopilot. Often this occurs when using a rally point as the common destination for many ships. This also can be gotten around by moving all the ships that will reach the rally point during the first turn after a reload by hand. It seems that it's the arrival of a ship at the rally point that causes other ships to forget their destination, but only for that first turn after a reload.
Also when using rally points you need to be careful about precisely what a ship/fleets destination really is. If you use the T keyboard shortcut or the ship/fleet menu to explicitly assign a rally point destination that is usually pretty reliable. However if you set the rally point destination by selecting the ship/fleet and then right clicking on the rally point and there are already ships at the rally point it's not so certain that the rally point is set as the actual destination. Sometimes the destination is set as the parsec itself (i.e. the x,y coordinates of the rally point) and sometimes the destination is set to be a ship that is sitting at the rally point.
What can happen is that you have the rally point set to fleet up ships as they arrive. In the meantime you set the autopilot destination of a ship/fleet to the rally point by right clicking on the rally point but instead of the rally point being the destination, the "real" destination is set to a particular ship that happens to be sitting at the rally point. Then the next turn some more ships arrive at the rally point and combine with the ship that had been set as the destination of the other ship/fleet into a new fleet. Now suddenly the single ship destination of the ship/fleet no longer exists and the ship/fleet "forgets" where it was going. Another thing that can happen when a ship gets set as another ship/fleets destination is that you move the destination ship somewhere and the other ships/fleets that had it as a destination will continue to follow it. This is actually kind of funny when it happens.
There are other situations where you're using colony rally points to get the autolaunch feature where ships built at some planets will just sit there and never move. Given that you do have to wait for end turn to get autopilot movement and given that you may be producing a ship at that planet every turn (or every few turns) it may be difficult to notice that certain ships have not moved during the autopilot phase until you happen to stumble on a planet with a bunch of ships piled up next to it.
In conclusion there have been a lot of different problems associated with autopilot over the course of the different versions of the game and even different revisions of the same version so it's important to be as explicit as possible when describing your particular problem.
In general I play gigantic galaxy games and produce many thousands of ships (on the order of 17,000 actually) and often have many thousands of ships all operating on autopilot at the same time and usually there is some method for you to do what it is you're actually trying to accomplish, however it often requires some fair amount of "hand holding" to get around some of the inevitable problems.