Published reports will try to open any connections to database servers when they are run. In the case where the server is not available, the report can not be opened.
If you need to download a report when it's in this state, then you can try the Rescue tool which will attempt to download the report without running it.
This means grid data may not be visible, but you can use the standard Excel connection screen to update the connection when you open the workbook.
If you use connection mapping, then you must set a web.config setting: UnmapConnectionsOnExport = false
Select the Parameters icon next to the report on the Home screen, under the ellipses ... and at the bottom there'll be a Rescue button that'll generate the rescue URL. Paste this into your browser and you will be prompted to download the file.
If the Rescue button isn't visible, you'd need to check that you have permission to the rescue.xml file located in xlcubedweb\xml\security. You can create the file if it doesn't exist and use the following for the content
<?xml version="1.0" encoding="utf-8" ?>