From: Dave Restall < email@example.com> RE :- Could it burn out through the ignition being on while the engine was off ?It depends. If the ignition is points based, i.e. not the VFR then yes it is possible - bit of a funny coincidence though that the same side fizzed twice.
Also, A LOT of older bikes use reactive ignition. In this case the points short out a coil within the generator. When the points open a large emf is generated by the coil which is transferred to the ignition coil. In this instance, there is NO DC supplied to the ignition system, it only gets power when the engine is running and that in the form of bursts when released by the points opening.
The only real risk of the coil burning out is when a DC current is passed through the coil that is BROKEN by the points. If the points are closed when the ignition is on, a current will flow until either the coil burns out, the battery runs flat or the points are opened (either by starting the engine or just spinning it over).
A typical primary resistance of an ignition coil will be in the order of 2-6 Ohm. With a 6V system and a primary resistance of 2 Ohm, you get a residual current of 3Amps. Your coil will get quite warm with this. With a 12V system, you get 6 Amps, or 72 Watts. Your coil will get VERY warm with this. These two examples assume that the coils don't have a ballast resistor.
When the engine is running, the DC is chopped so that the "average" current is much lower than the steady current - also there is the effect of the coils inductance to take into account when passing a varying current to it. Basically, the coil is a different animal when DC is passed through it than when a chopped DC is passed.
Again, why it should burn out one side is a bit of a mystery, however, most engines tend to have a "favourite" stopping position which on cars is usually characterised by heavier wear on the flywheel starter ring teeth. It may be that your engines favoured stopping point is with the points for the offending coil closed.
As an aside on CDI systems, the primary resistance of the coil is about the same as for a normal points controlled system.
Voltages this high as you can imagine are pretty hard to contain in a confined space, and "leak" out with very little provocation. This is why touching an HT lead can result in belt when the engine is running even though the lead is insulated. With this problem, the insulation in the coil itself has to be as near to the perfect insulator as possible. Normally, the coil is wound with very fine wire that uses for its insulation - wait for it varnish : and not very thick varnish at that. Insulation breakdown of the varnish is a pretty rare event - it's slightly better quality than the average tin of Dulux - but it isn't unknown. What happens here is that a hole appears in the varnish and the electricity "leaks" out, normally in a spark form between the windings. This in turn punches holes in the insulation of the destination of the spark which leads to more "leaking" resulting a severe deterioration of the coil's performance.
What may be worth looking into is whether water has got into the coil. Water in the secondary of the coil will also cause leakage. When I say water, include condensation - so the water could be getting round where the HT lead leaves the coil. Try drying the coil out by leaving it in a warm place (on top of a CH boiler for a few days) then seal all orifices on the coil with vaseline (Let the coil reach normal room temperature first).
This may revive the coil.