lefteris
Make a VERY simple CSV file that imports one item. No custom post or anything just the most basic import to test if that works. Ideally test it on a not nginx instance to make sure the plugin has no issues with the file.
If the test file works on your problem site, the issue is you need to increase some php limit in php.ini file. Among others, it could be max post size is too small for real imports.
If it doesn't work, something is wrong with your nginx config but that would most likely be breaking other stuff too.
