I just had this happen, and here's my workaround. Basically, an APRX file is a zip-compressed folder, consisting of (among other things) a folder for each element of your project: map, layout, etc. Inside each are XML files and such defining the setup of each element. Chances are, one of those elements is corrupt. So, use the "Christmas Lights" method!
- Copy the APRX file
- Rename the copy to .zip
- Open the zip file, and delete one of the folders
- Rename the copy back to .aprx
- Try to open it in ArcGIS--if it works, that's the offender, if not, repeat steps 1-5 for the next folder.
Yes, you can speed this up with a binary search method to narrow it down (delete the first half of the folders, then the second half, ...), but remember that there may be more than one corrupted element (the christmas lights nightmare). Once you narrow it down, you could go into that folder and muck around looking for the problem, or if it isn't too major (my last one was just a selection set, so nothing major), just leave it out and build that element over again. The fact that the master XML file is now referencing a missing element may or may not throw an error or a warning, depending on how vital it is, but in my experience, it seems to make do okay.
