Answer
Change the 'Cleanup age limit in days for application message statistics' setting in System Parameters to a larger number of days — this directly controls how long application messages are retained before cleanup. A restart of the middle tier application may be needed for the new value to take effect. The main tradeoff is that retaining messages longer means more accumulated rows in the underlying application message tables, which can grow the database and slightly affect query/cleanup performance if left at a very high value for a long time — so pick a retention window that matches your actual troubleshooting/audit needs rather than setting it arbitrarily high.