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 is 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
Click the "Parameters" icon next to the report on the home screen (under the "...") and at the bottom will be a "Rescue" button that will generate the rescue url. Paste this into your browser and you will get prompted to download the file.
If the "Rescue" button isn't visible then 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" ?>