Is there a way to recover a non functioning aprx file?
In ArcMap you could use mxd doctor, but from what I've seen ESRI don't have anything like that for ArcGIS Pro.
There is an existing ArcGIS Idea titled APRX Doctor:
It would be great if there were an equivalent to MXD Doctor for ArcGIS Pro projects.
which has been Reviewed but which does not yet appear to be In Development. I recommend adding your vote to that and, in the meantime, as @Mapperz commented:
the dump log is the best bet so far C:\Users\username\AppData\Local\ESRI\ErrorReports