My observations of your site:
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the repeater, and its embedded components, are connected to a dataset
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the embedded components are not connected to any fields of the dataset’s items
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you are also doing a query on the collection and then manually setting the repeater’s data based on the query results
Some issues to consider:
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connecting the repeater to a dataset and manually setting the repeater’s data causes a conflict
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by using just a dataset, but not connecting the repeater’s embedded components, the components will not get any content
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Preview and Live have different paths for rendering, which is why it works for Preview, but not for Live
Try removing the Repeater’s connection to the dataset and try again.