If you have multiple old sites in your “Organization-Sites”
you can try to delete in Rich Client.

But sometimes a site has a reference to something you cannot delete.

Go SQL Management Studio and select your Database
(do this not in operation and make sure you have a proper backup)

-- Search for site_puid
select * from PPOM_IMC;

Copy the puid of the old site you want to delete.

-- then look for referene
select * from POM_BACKPOINTER
where to_uid='PasteYourUID_Here';

All listet entries are objects in the dabase which are linked to the site.
you can use this UID in Richclient to search for (Window-Show View-Other-Diagnostics-Print Object)
If you sure you can delete all these references:

-- delete all references 
where to_uid='PasteYourUID_Here';

Restart your RichClient and try to delete the Site in Organization.