I just went through the code – everything looks good – however I can see where this could happen due to file permissions on the file system.
It looks like this property is persisted to the dataimport.properties file in your conf folder. If solr can't write to this file, it will appear as if the last_index_time is not updating.
Code was added (not sure when) to surround this persist call with try/catch and add a status message "Could not write property file. Delta imports will not work. Make sure your conf directory is writable" if it cannot persist the file.