In this case, the customer had several different license servers set up in his company, and he noticed that one license server in particular was very slow. When he used that license server, all his Autodesk software took a long time to start up.
Also, there was another symptom: he had to use the IP address to specify the [slow] license server location. If he used the name of the license server, the software wouldn’t find the license server.
Ultimately, the problem was solved by installing the IPv6 update for the Autodesk Network License Manager.
Disabling IPv6 on the client may have also worked.
I don’t know that there is a general problem related to IPv6, but I did find a handful of other, similar support cases logged over the last couple of years. There were a couple about slow license checkouts, and a couple about having to use the IP address instead of the computer name.