make sure your attachments in vB are set to database? lol. same with avatars? i had issue with importing to burning board from vb4 because the files weren't stored in database...custom avatars, avatars, and attachments need moved from OFF server storage to the database storage.. THEN did import and it worked fine. but like jake below said, just refresh page
What is the error message? What is happening exactly?
For a large import that is encountering problems it can be a good idea to take backups throughout the import so you don't have to start over if you encounter an error. But even if you get an error you should be able to just refresh the page. It will pick up where it left off. Don't close out the import because you can't reopen it.
I did my vb3 convert at home (I think I had about 20,000 attachments then) on a generic server setup on a decent PC, changed the hosts file so I could use my domain... once it converted well locally I simply moved the new xenforo package and database back online. Trying it 'on the fly' maybe not such a good idea, it's a lot to process and you want all your resources focused on doing it.