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For more on marking an answer as the "Best Answer", please visit our FAQ.Unless you have an intermittant earth fault somewhere in your electrical system, maybe the cable has corroded so badly that its effective conducting area is reduced. This would cause its resistance to increase and therefore it will heat up and blow like a fuse if the damage is bad enough.
I think that the cable will need replacing. Taping it up will give you a high resistance joint that will eventually fail (probably just when you don't want it to). A good look at the heavy wiring around your battery and to the starter motor would be a good idea too.