The common issue with the importing demo is a few server resources. I suggest you check this out with your webhosting provider too.
The import process is quite a heavy and resource intensive operation. WordPress needs to import all posts, taxonomies, terms and download attachments. These resources are allocated based on the server configuration. You could ask your webhosting provider to kindly set in the php.ini file these values:
memory_limit 256MB max_execution_time 300 post_max_size 20MB upload_max_filesize 20MB
In most cases this will solve the issue.
NOTE: it is very important to import data on a clean WordPress install. This will save you from many possible issues.