Based on your site info, was the posts table called "BJJQVpSXposts" ?
The list of importers is generated based on that table which is why i cant understand why they dont exist, because if it doesnt exist then it would not be displayed.
Are you able to go into Tools > ImportWP > Settings / Tools > Import / Export > Export Importers , and try to export your imports.
The only way i can see me being able to help you any further would be if you are you able to provide admin access, ftp access and database access to your site, so i can get a better understanding of what is going on as this sounds very specific to your website.
Thanks
James