They really do have some sort of transistorized ignition box. It helps the
points. Inside the box are several electrical components that can fail due
to corrosion or old age. That could cause the intermittent problems
bescribed. These boxes are really expensive new. You can try to find one
second-hand, or try to replace the electrical components inside the box if
you understand what they are.

If that doesn't help, it's also possible to rewire the ignition so that you
donot use the box. Just wire the ignition like any standard points ignition.
In that case, you will be chanching points very often, because they will
wear much faster.

Hope this helps,

Paul