If possible save your database to your main hard drive rather than a network drive; an external drive should be OK, but ideally the main drive. Make sure you have enough space to save the backup, and some spare - PostgreSQL will work much faster if there is plenty of free space on your disk.
Try disabling the 'Optional Files' and just back up your database. If that works, try another backup with just the Optional Files and no databases.
If you still can't get the backup to work please enable logging (Configure > Options) and restarte PT4. Try the backup again then attach the PokerTracker4.log file from C:\Users\yourname\AppData\Local\PokerTracker 4\Logs (which you can access from the PT4 File menu) to a
Support Ticket so that we can see what is going on.
Tell is in your ticket if you are able to start the backup and then it stops responding, or if the backup window does not load properly.