Thanks for posting the issue here!
Please perform the following and see if it helps:
In the your collection database, open the tbl_Version table and within this table you will find that these folders were referenced in the fullpath (ie if the folder was called ‘FolderThatWontGoAway’ in Team Explorer, then this was ‘$/FolderThatWontGoAway’
in the database. By simply changing the deletionId column in the row of this item to a valid deletionId value (value other than 0) the problem was fixed.
Hope it helps!