A ready export shows a countdown like "(Expires in 5 days)" so you know to download it before the 30-day window closes. Once it ages out, it consistently reads "expired" with a note to contact support for a re-run.
A completed export shows how long remains to download the file. Your team can use this notice to collect the data before the link is no longer available, rather than discovering the expiry when opening an older request.
Open Reporting → Conversation Export and check the completed request in the history table. Download it while it is available. If the row says expired, contact support for help with a new export of the same period.