You may want to make sure that the connection file is saved in a public location, not your local profile. In Excel, on the Data ribbon click Connections > select the connection, probably called something like owssvr, and then click the Properties button. In the next dialog, click the Definition tab. Click the button to Export the Connection File. Upload that file to a public location, for example a SharePoint Data Connection library. Make sure that the file is published. Then, back in the Excel file Data > Connection > Properties > Definition > Click Browse, navigate to the SharePoint site and library and select the published connection file. Save the Excel file.
Users need at least read access to both the Data Connections library and the SharePoint list that the connection file points to.