Also, (I am not an expert, so please check with others) the DWELL when contacts are closed is important for the coil to get sufficient magnetic charge to achieve the required voltage when they OPEN to discharge across the Spark-plug (or other weakest point of resistance).
Detail:
The coil is an inductor: (Sorry if I am teaching the experts my lack of understanding?) so Inductors start at high voltage when the contacts close and 90degrees out-of-phase they are at "zero" current, but rising rapidly (Held back by the back-emf of the inductance of the coil). The energy stored in the coil is proportional to current, so the contacts need to close for long enough to charge the coil. Then when the points open, the coil wants to dump all that energy - and does so across the easiest path - which is the spark-plug gap if all other resistances are big enough. But if the contact gap is too small, then the energy may arc across this gap as the resistance of the air can't resist the voltage of the primary coil. - Or if you put a big capacitor across the points it will rush into the capacitor instead! - So insufficient spark to ignite the fuel-air mixture. Incidentally the fuel air mixture at 10:1 compression has effectively 10 times the resistance of the same gap in ambient air. Hence the need for the coil to generate a few thousand volts! (to jump a 25 thou gap) compared to the primary voltage being 6 ~ 12V. (across the 15 thou points gap). At the points, the arc starts when the gap is just forming - less than 1/10th of a thou - and the ionised gases then conduct the arc as it is drawn-out with the points gap opening. If the gap opens quickly, it will cool the arc quickly as it is drawn-out, and naturally will quench as the incoming gas is resistive, as opposed to the conductance of the ions from the arc. But if the spark cannot strike on the spark-plug, instead of most of the coil's energy being dissipated across the spark plug, it all dissipates across the points - burning the contact points rapidly.
Or at least I think that is what is happening?
So you may be able to get a "Dwell meter" to check what your points are doing? (Motor Racing tuners usually need them).
And please check the capacitor across contacts is a correct size/type? (I had one partly fail on a Honda, and blew the exhaust silencer open with the mis-fire!).
And check points gap versus coil type and compression ratio? - Are the points showing signs of arcing? (Use a magnifying glass).
Finally, check the spark plug type and gap is appropriate. (A wrong plug type stopped my mates 2-stroke motorbike from running, but it always started easily.).
If you have "suppressing" HT leads, or plug cap. then that may also be the problem. (I had a mis-fire on my motorbike due to a suppressing plug cap being over 15KOhm, not the designed 10KOhm.).
Maybe the battery can't sustain the current required? - I have a digital radio that takes disposable batteries - then eats them - but hardly works at all with rechargables, as they can't sustain the voltage (which is 25% lower anyway). So maybe you need NiCads, not Nickel-metal hydrides?
K