By design, exporting comments into Excel is not possible in OnDemand. That is most likely due to the varying amounts of data being copied into cells.
In any case, the recommended approach is to manually create a backup - you can then retrieve the data for safe keeping or it can be used to import into another JIRA instance for example.
This how-to doc should get you on the right path:
Hey Atlassian community, I help lead engineering at Sentry, an open-source error-tracking and monitoring tool that integrates with Jira. We started using Jira Software Cloud internally last year, a...
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