@ Adam
Sounds as if there is either a fatal javascript error occuring OR the server is responding with an invalid response.
Try this, use Chrome for the import. Load the first step of the import in Chrome (where you choose the file) and hit the F12 key. Choose you file and map as you’ve done previously. On the last step, the please wait, click the Console in the section shown when you hit the F12 key.
Are there any errors shown? If so, what are they.
Now, click the Network tab. Scroll towards the bottom. One of the last rows should be a reference to admin-ajax.php. Click that row. There could be several for you to review, but only one should be related to the import. Find that one and review the details by clicking on it. When you click on a row, the details will be shown. You’ll see the sub-tabs will be Response and Preview. These are where you will find errors.
Can you find any errors? If so, what are they.
You should also enable PHP error logging (not displaying errors). After you do an import, review the log to see if PHP is reporting any errors.
Lastly, try installing the 2.0-RC version of the of CSV Import instead. It provide more feedback and there is no need to not map the entry id.
Let me know what you learn.
