To keep your site operating at optimal speeds, we keep the timeout value on the server fairly low.
If you get an error when using the WordPress importer (Tools > Import) to import your posts when migrating your WordPress site, just hit refresh once and wait. When the page is done loading (you will usually see a spinning icon or lower left corner of your browser that says "waiting..." if it's still working on something), hit refresh again if needed and wait.
It is not uncommon to have to do this 2 or 3, or even 5 times when importing a few thousand posts.
Eventually you will see the WordPress dashboard again and the "All Done, Happy Blogging" message.