I have the latest version of Autodesk 360 and I am using Autocad LT 2014.
There seems to be no pattern for when the Sync gets stuck, but occasionally Autodesk 360 will sync indefinitely and it causes AutoCAD to run extremely slow. Restarting the computer fixes it but it has been happening a few times every week. I have attached my ADSync.log file for review. I have also had the folks on Twitter @AutodeskHelp looking at the issue and they wanted to see the log file.
I have also attached an image of our Twitter conversation.
Thank You!!!
-Tony