There are going to be known possible courses. On a bigger scale, there is the Interplanetary Transport Network, using gravity assist and Lagrange Points to move between different planets with the minimum of fuel. The theory for this navigation already exists.
Telescopes can be used, to track the reflection of the ship. As it moves, you would be able to predict it's route, within reason. Straight (well, curved with gravity) lines are going to be the norm, as changes in direction cost fuel, and that's a finite resource.
Transponders are good for tracking. Over that distance, the signal is only going to be few minutes old, but is subject to interference -- dust, rocks, planetary bodies. Best thing would be to have multiple receiving stations, e.g. one on the moon, one in the Sun-Earth Lagrange point, two or three on Earth, another couple on Mars. They could all be dedicated to tracking craft, similar to radio telescopes working in concert.
The 'ping' is the most subject to failure, as it's a machine. Transponders do fail. Comms cut out. Albedo reflection is variable but, once you know what to look for, you can find it again (that said, astronomers have lost a few asteroids over the years, so...). A ship's course between A and B may have variables, but alter it too much, and you go off Into The Great Wide Open. Of course, if those tracking the ship did lose sight of it for a long period of time, they might believe that was what had happened.