It sounds like the K2 server and K2 for SharePoint are out of sync; i.e. K2 is attempting to call a nonexistent method in one of its web services in Sharepoint.  If you have recently upgraded, make sure that all of your SharePoint servers are upgraded to the same K2 version and that the K2 for SharePoint Configuration Wizard in Central Administration was successfully run to completion. Also, it is sometimes necessary to retract the existing K2 for SharePoint features/solutions, remove them from the farm solution store, add them back from the latest copy of the files, and redeploy them.  Here's the guide for manual deployment: http://help.k2.com/en/displaycontent.aspx?id=4102

If you haven't already, you can run advanced logging to troubleshoot further : http://help.k2.com/helppages/k2blackpearlicg4.6.8/webframe.html#troubleshooting_enablek2logging.html