Mudbox uses the same licensing procedures as other Autodesk products.
In a network licensing environment, if the connection to the network server is lost, Mudbox attempts to reconnect to the server for 120 minutes.
If the connection has not been reestablished after 120 minutes, you have a ten minute grace period in which to save your work.
Once the grace period has ended, you'll be prompted to save your work, and the software will exit.