You definitely need a battery, as you're likely to killth eignition unit (PGM) without. The battery has a tendancy to take the rough edges off the generator output, as well as provding power to the circuits when starting. I'm impressed you started it at all!

It could be fuel starvation, have you checked that the feed hose from tank to carbs is in good condition? I have heard of them swelling and reducing fuel flow when old.

Otherwise, it may be something electric getting hot and breaking down, like the spark plug, cap or lead. Have a good look at the cap and the connection to the lead, as well as the coil and it's electrical connections to the loom.
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