Well, whatever is happening is not happening at the runtime-level. The only thing I can think of now is to get a memory dump.
Extract all files to disk, open a command prompt and run
cscript adplus.vbs -crash -pn RedGate.Profiler.UI.exe
If profiler exits unexpectedly, there should be a full dump file created. We can have a look at this and see why the runtime stopped.
I can set up an FTP account for you to upload it to.