If you are having network reliability issues:

1. speak to your network/SAN team (and/or use a different file share that doesn't exhibit the problem)
2. Back up the file, **temporarily**, to the local SQL Server system, assuming there is adequate space. Then copy the backup to the network share, and delete the original when the copy has been confirmed. 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.