A few things to try. I recommend 128MB of memory allocated to PHP. The memory could be running out during import if the value to too low. I recommend setting the execution limit to 300. The import does try to do these automagically, but some hosts do block attempts to do this.
Another plugin or the theme could be causing PHP notices which could break the AJAX process required for importing.
Here’s a list of FAQs that covers these.
- How do I increase the WordPress Memory Limit?
- How do I increase the PHP Execution Limit?
- How do I hide PHP Warnings and Notices?
The easiest solution could be to deactivate all other plugins and do the import and then reactivate them all.
If you want me to take a quick look and attempt to import the file I’ll need a template admin login. Details can be posted here as a private reply.