After in place updating concurrent use ArcGIS Desktop from 10.4.1 to 10.5, all my Folder, Database and GIS Servers connections are gone. Is that a new workflow?
This used to happen in earlier versions as well. When an upgrade is done, the ArcGIS Application profile gets reset alongwith registry changes. So, everything starts afresh. You could take a backup of these folders from previous versions before upgrade and replace them after the upgrade for keeping the customization intact (ArcCatalog Folder, in this case, located in C:\Users\<UserName>\AppData\Roaming\ESRI\Desktop10.4.x.)
This blog post may help.
Retrieving data ...