This issue has been escalated as bug report to Evernote support last week. Today, I received a reply that the bug should has been fixed via yesterday update. So, try to use the latest client version.
I have found the solution by reading other topics in this forum. I have the same problem on my Xperia Ray phone with Android 4.0.4. The last sync failed when downloading header at 35%. Then I open my laptop and empty the Trash on the Evernote Web. Suddenly, the sync works again. Note: that is the only solution that works. I have tried installing previous version via AppSaver, clearing data, reinstall, relogin.... etc. countless times. Thank you.