This behaviour relates to how the Analytics bar on the search dashboard uses the response query rather than the parsedQuery.
The "Full Analytics" link looks for Analytics data using the raw query value, as opposed to the normalised parsedQuery. This differs from the main Analytics dashboard, where data is stored and aggregated against the parsedQuery. This is the expected behaviour, based on how the Analytics bar currently processes queries.
When a rule is applied that replaces a query, the query in the response reflects the replaced query. As a result, the Analytics bar attempts to retrieve analytics data for that exact string, including quotation marks and capitalisations. Because this lookup is literal, if often fails to find matching analytics entries and so the dashboard displays N/A.
For example: mens sweaters is replaced by sweaters for men
If the replaced query includes quotation marks, the discrepancy becomes more apparent.
For example: womens sweaters is replaced by "Sweaters for Women" - analytics data does not exist for the capitalised quoted query, so no data is shown.
This same behaviour can be seen even without Rules by directly searching for a quoted query - the Analytics bar uses the capitalised quoted query.
For example: