One thing to check is the disk drives. I have had rsync stop when it reaches
corrupted sectors, especially if those sectors corrupt part of the file
system. I don't remember anything helpful in the log files, I just noticed
that it wasn't finishing. Try running disk diagnostic software and make sure
your hardware is good. What kind of hard drives do you have and what OS?
If that doesn't show up anything, I would start by synching just one folder.
Create a test folder on both computers and add a few files. Make sure your
permissions are correct. Make a change in one file and then run rsync. If it
finishes and the logs look good, add more to the test folder and see if you
can find where it brakes. You can test things like very large files, and
folders with a large number of files. If you can't get it to fail, then the
issue may be with the data on one of the computers.
The problem may also be with the rsync software, but I can't advise well on
that end.
LMH