Import process needs server to support full import.  Many shared hostings limit services such as: Your PHP memory, file upload size, and/or execution limits are set too low. And these have to be corrected by hosting on in your hosting account (if your hosting allows you to do that).

Ideally these values should be:
max_execution_time 180
memory_limit 96M
post_max_size 32M
upload_max_filesize 32M

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How To Verify Your Current PHP Limits

Even if you make changes in wp-config, it is very possible the limits do not change because your server is limited from server settings. You can verify your PHP configuration limits by installing a simple plugin – https://wordpress.org/plugins/wordpress-php-info/

If you see limits don’t change you can always contact your host and ask them what the current settings are and have them adjust them if needed.

Please note though that many hosts will try to keep the PHP limits.

These are the first settings that should be checked and edited on server for import to go through.
When we meet with clients that have issues importing demo we cannot do any server change for them. Each client must check server changes and requirements.
From theme end we can try to repeat import (if it stops often during import) and repeat does the trick. If after 5 times it is still not going through – please check above settings and try again.

After you change the settings we can try as well. For that please open a ticket in our client support system with your site url and wp-admin – http://support.wpestate.org/