I've got the same poi and when I got them I saw the same problem. The attachement ring is made of the same soft material so i tought it would be a problem.
Till now i only prevent the damage, i had splitrings to attach then on the cords, but they damage the material so i got quicklinks.
If you got the same pastic material like mine, you could try glue like silicone kinds, or normal fast glue or ductape? I'm a fan of ductape, it's something everyone who performs should have in his suitcase.
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Without Poi in heaven, I won't go!