I appear to be running a beta copy of Origin (I have no idea why, I'm not sure I asked for it) which offered to sync my Mass Effect 3 save games to the cloud. Unfortunately, after a 12 hour playing session, it appears to have deleted my save game rather than syncing it. Is there any way to recover my progress?
I would recommend using Recuva to try and restore deleted files. Super User might have some more extensive advice regarding restoring deleted files. I am not an expert on Origin, but perhaps there is an option to manually trigger the sync to download the saves from the server, provided it did upload them there.
As it happens I was able to solve this problem because I store all of my game save files in Dropbox, which I have discovered gives me the ability to undelete deleted files and directories, so while this worked for me, it isn't of general usefulness.
I do, however, recommend storing save files on a cloud storage platform for easy transfer between machines, backup and now for precisely this sort of situation. In the case of Dropbox, it is necessary to create symbolic links from the place where Windows expects the save files to be to the Dropbox.
To do this, one opens a command prompt Window with adminstrator privileges:
These instructions for Windows 7/Vista. Everything except the "mklink" command can of course be done using the GUI.