This issue occurs when the conversations contents are larger than 1 megabyte (MB) in Microsoft Lync 2013 (Microsoft Skype for Business). When this issue occurs, history conversations aren't saved or uploaded to your Outlook Conversation History folder.
This issue occurs because the size limit of a history conversation file is 1 MB. When the limit is reached, Lync 2013 (Skype for Business) can't upload the conversion to Microsoft Exchange Server.
To fix this issue, install the November 10, 2015 security update (KB3101496) for Lync 2013 (Skype for Business).
Note Lync 2013 was upgraded to Skype for Business in April 2015.