There's some issues with the server then... really, the script is dumbed down quite a bit to run on shared host platforms. As long as the forum is turned off, the amount of server load should be less than the forum running at other times normally with users posting and etc.

Now, you mention the upgrade tool, are we still discussing the importer or the upgrade? Upgrading is a bit different and for some versions being upgraded it's possible to tank a large forum when indexes are being added/ updated/ deleted. The original topic is regarding the importer tho.

In such a situation you could use the method that Sirdude described here, make a backup, run your importer locally, and transfer that data to the actual server when done.