Can want retain the old issues(defects) which links to Jira in each new test cycle?

We create new issues(defects) during each regression test cycle, but the issues previously created which associated to the test case are wiped out every time a new test cycle is created. can we retain those old issues and carry them over to a new test cycle for reference purpose and to see the status of the old issues to prevent us from create duplicate issues? This feature is extremely helpful to see how often defects reoccurring.

Sarah