KB3097645 fails even at the second attempt.
KB3097645 will run an Install-CsDatabase command to patch the database.
If you look at the log found in the same directory as your SkypeServerUpdateInstaller.exe
You will find the following error messages:
[12/8/2015 2:00:01 PM] Executing command: msiexec.exe /update "C:\temp\Server.msp" /passive /norestart /l*vx "C:\temp\Server.msp-FE01-[2015-12-08][14-00-01]_log.txt"
[12/8/2015 2:00:23 PM] ERROR 1603: Server.msp had errors installing.
[12/8/2015 2:00:41 PM] ERROR: SkypeServerUpdateInstaller failed to successfully install all patches
If you look in the file LCSSetup_Commands.txt found in the user profile
You will find a more understandable error message:
Install-CsDatabase : Command execution failed: Install-CsDatabase was unable to find suitable drives for storing the database files. This is often due to insufficient disk space; typically you should have at least 32 GB of free space before attempting to create databases. However, there are other possible reasons why this command could have failed. For more information, see http://go.microsoft.com/fwlink/?LinkId=511023
The solution is of course to simply free up some disk space or expand the disk.