Full Back up over to Network failed due to unknown network error 59
If you are having network reliability issues:


speak to your network/SAN team (and/or use a different file share that doesn't exhibit the problem)
Back up the file, temporarily, to the local SQL Server system, assuming there is adequate space. Then copy the backup to the network share, typically using a tool that can resume interrupted transfers, and delete the original when the copy has been confirmed (which usually includes validating that the backup can be restored). If a copy fails, no big deal; you just start the copy again, and you haven't lost anything.


And I agree with Max, this doesn't seem to be something that altering a session timeout will fix; that's kind of like changing a tire when your headlight is out. You might be better prepared for the next pothole, but you're still only driving with one light.