To install a free academic license, the computer must be connected to the university network, via either a physical connection or VPN. If you use VPN, the connection to the Gurobi servers must go through the VPN.
It is not uncommon that the traffic gets split up via split tunneling and not all your internet traffic is directed through the VPN connection. In order to force the traffic to not be split, please see, for example:
Once the license has been installed successfully, a connection to the university network is no longer required. If your computer cannot be connected to the university network, contact email@example.com for assistance.