"Connect to Outlook" button disabled on an External List based on "Contact"

I'm using SharePoint's Business Data Connectivity to connect to external source with contacts information. I created a .NET Assembly connector (BDC Model project in VS) with ReadItem and ReadList methods. I have deployed it and I can see my External Content Type present in the Central Admin.

Then I went to SharePoint designer to associate my new content type with Office Item Type "Contact". I have successfully mapped the fields (FirstName, LastName, FullName, Address and Phone; ID is mapped to "Custom Property") and saved it.

Then I created an external list based on this external content type. It works fine but the "Connect to Outlook" button is disabled.

I have the feature "Connect External Lists to Outlook" activated and also "Offline sync" in the content type in SharePoint Designer is marked Enabled. If I create a normal Contacts list "Connect to Outlook" is enabled and works as expected, so no problems appear with the machine itself or Outlook. Where is the problem?