Mysterious permission denied
Omnigraffle attempts to save its files as packages - a format OS X supports, but windows and samba servers do not.

There is an "save this document as a flat file" preference option for each document in Omnigraffle which should resolve this issue and should be used if you regularly save to network shares on non-Apple servers.

http://forums.omnigroup.com/showpost.php?s=c1d4e102eef15890d2c46830044899aa&amp;p=52096&amp;postcount=5

You'll need to change the document properties for each document you wish to save this way:


  You can go in to the Inspector for the document, and look in the Canvas accordion pane under the Document Settings tab. There, you will find a heading for "File format options", which by default seems to be set to "Automatic." You can change this to "Save as flat file", and save the document


If you need to do this often, you can change the document templates so that any new documents you create will automatically be flat files:


  
  Go to the OmniGraffle application bundle, right-click, and select
  "Show Package Contents." 
  Finder will show you the inside of
  application bundle. Navigate within the application bundle to Contents
  => Resources => Templates. In here, you will find a set of OmniGraffle documents that are used as your default document templates.
  Open
  the document template that you want to modify. OmniGraffle launches
  and shows you the document. 
  Open the Inspector for the document, go
  to Document Settings under Canvas, and set the document template
  file's File Format option to "Save as flat file." 
  Save the document
  template.
  
  
  Now, all new OmniGraffle documents created from that document template
  will also have their default preference set to "Save as flat file"
  since the template's preference has been set to that setting.


(via maxim porges)