@KoCo
first try restarting Alteryx and then if the issue persists Try re-authenticating the connection to the Tableau Server on the affected desktops. Sometimes refreshing the authentication token can resolve such issues.
hope this helps.
"refreshing the authentication token" being a change of the password?
Is your Tableau server in a VPN? are there IP restrictions? Are some users on your VPN? Going a different direction from @Raj here - if some users can connect and some cannot - this sounds like an internal traffic/VPN issue.