If I adjust tension so the cable is slightly taught when the door is open then the door only closes about half way. If I adjust tension so that the door closes all the way then opening the door creates so much slack on the cable that it falls off the drum.
Do you have the right size and number of torsion springs? If your spring is too strong then that might explain this behavior.
Either the spring isn't capable of doing it's job, because it's
- the wrong spring
- loose or sloppy on the shaft
- it has two springs and one is broken (or the installer omitted it)
- the drums which take up the cable are the wrong size
- you did something that significantly changed the weight of the door
Or, you have rather high drag in the mechanism, owing to:
- a trammed door (the door is trying to rotate because the side cables are not adjusted to the same length, and so the spring is not picking it up on both sides equally)
- a drum that is loose or sloppy on the shaft, causing the above
- dirt in the door tracks
- dirt in the door rollers
- worn out or beat-up door rollers
- damage to the track
- foreign objects hitting the door and dragging as it passes
- a garage door opener putting drag on it, e.g. Dirt or rust in the opener track/chain.