Well, it does rather sound like a spark problem, but one hesitates to try to be too specific when there are obviously other possibilities.
However, I wonder what 'refurbished' means ref the mag? Was it rewound, new slipring and condenser etc, would be my first question? And decent pick-ups and brushes?
First thing to do is see whether there are sparks next time the thing is hot and won't go, as suggested. That's easy to do (especially if you have a 'large block' to drive round and round, within walking distance of home!)
If there are no sparks, then almost for sure there's a fault in the mag. Assuming the points are clean, opening, gapped reasonably correctly . . . . Typîcally, a faulty condenser or a defective HT winding. For a quick test on the latter - I'd take off a HT pick-up, turn the engine till the brass track of the slipring is visible down the 'ole, and measure the resistance between the brass bit and the mag body. You want to see, in round numbers, about 5000 ohms. Open circuit indicates either a fault on the HT winding or a poor connection of coil to slipring. With any luck, it'll be OK, if it passes that preliminary (but not definitive) test. (If the coil is an original, there could still be an insulation problem even if it remains continuous, it does have to be said.)
The low tension will almost certainly be OK - measured from the cb centre screw to earth with the points open, about half an ohm.
You can't test the condenser with it in situ though.
If you get the mag off the bike, you can do some quite useful testing with a drill, and borrowing the domestic oven, or using a heat gun in a confined space. You want to get the thing soaked through to about 50°C - not all that hot, but uncomfortable to handle for long. Then stuff it in a vice, and spin it with a drill. If a drill with variable speed, you should be able to go slowly enough to see what happens at tickover and kickstart-type speeds. If you can turn it so that you are getting about 2 or 3 sparks per second, using a wrist watch to count, you are around 'right' - but you want them to be decent fat sparks. One way to get them is to grind the earth electrodes off a couple of old plugs to get gaps of about 4mm, which is better than nothing. The test spec of Lucas was for 5.5mm gaps - but using pointy three point needle-type things, across which sparks hop more easily than from chunkier bits of electrode.
Cold, I bet it does the right thing from all you say, and you can count the sparks, and none or few are missing. But as it warms / when it warms, it may drop off badly, until you need 500rpm or more to get anything, and the sparks don't look as useful. In which case, you're into condenser or coil trouble probably, or both. Or, just possibly, you've got soft brushes and lousy cheapo pick-ups which lack the 'dielectric' strength of the proper items. Trying different / new ones might help, but if it's both sides at once, unlikely to tbe the (sole) cause.
Best of luck,
Bill
