I have fixed this issue.
Andy, you had pointed me in the right direction. However, because I had read this article before I posted and it didnt work, I disregarded it. However, there was a little bit at the bottom of that article which I did not read and this is what sent me on
the right path.
FIX:
I was getting Event ID 8123 and and 513 in the event logs.
It's easier to clear the event logs and restart the Cryptography Service to see what errors it throws.
I tried following
this article but it didnt stop event ID 8123.
I then used REGEDIT and went to
HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\VSS
and gave NT SERVICE full permission to this folder and sub folders. For good measure I ran the commands specified in the above link and this stopped this event happening.
System Writer still wasn't showing.
After searching high and low on the internet I found I had to browse to
C:\Windows\Microsoft.NET
Within this folder I had 4 folders.
Go in to Framework and Framework64 (I had to take ownership)
Look in each folder starting with v1, v2, v3 ,v4 if you have them.
Find the folder called Temporary ASP.NET Files (in each one) and delete all files and folders in there.
Run the above script again for good measure and then restart the Cryptographic Service.
VSSAdmin List Writers now displays the System Writer and i've successfully done a System State backup.
***UPDATE: Over the weekend the backup worked fine and then the System Writer disappeared again. The issue is down to the Temporary ASP .NET folder becoming too long. Clearing this folder out again restores the writer.
As a workaround you could create a powershell script to automatically clear out these folders. However, you should find out what the cause is. I will be creating a new thread as I think this is IIS related.
Get-ChildItem “C:\Windows\Microsoft.NET\Framework*\v*\Temporary ASP.NET Files” -Recurse | Remove-Item -Recurse
UPDATE: See
here on how to permanently resolve issue with temp ASP.NET files causing system writer to disappear
