Jules - you're not doing anything wrong. Some beads just break
I've had the same thing happen to me, and I have to confess that one one occasion I did just as Jason suggests. Set your wire in place, glue (this is one of the rare times when superglue works just fine), include the broken off piece if it's intact, and hide it all with the wrap once it's set.
Looking at the picture, I'd say they were only glass to start with, so your option is to be completely up front with the customer and explain that one broke. I'm sure she'll understand.
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