Antivirus scanner definition file update failed

Thanks to everyone contributing to this thread. It has been most interesting to see the suggested solutions to this problem.

To review, my issues started immediately after I updated to the latest firmware 6.10.3. I am convinced this update is a factor in all this. Immediately after intallation things started going crazy. My Time Machine (Mac) backups stopped working and would not recognise my passwords. For a while the RAIDar app was also struggling to find the NAS and again, for a while, I could not get access to the admin section/page on the browser. Multiple restarts/reboots eventually resolved a few of the issues. Then, for a while, I could only get my data LUN's to display on my desktop one at a time. Sometimes the NAS would completely disappear from my network. GRRR!

Then came the error messages. Firstly, the dreaded AntiVirus definitions failure to download. Then a few days later a new error message advising that my System root memory was almost maxed out. (Diagnostic test showed 92.2% full.)

I started following this thread hoping to be able to get a solution, but for me, realistically there was nothing helpful, because I have absolutely no knowledge, skill of confidence in using command level instructions or SSH etc. Although many of the responses were very clear and concise with the exact commands required, most of it was like an unfamiliar foreign language. Terms like Freshclam and crontab are a complete mystery. Did I mention that I have zero knowledge and skills of command level stuff and how to even get there? I bit the bullet and paid for a support case.

The tech's did much of what has been suggested. I downloaded my log files and opened the Secure Diagnostic Mode back door. This allowed them to see some errors. I was subsequently asked to turn Time Machine off because somehow the files that it generates had been written to the wrong place/folder?  

The two main error problems, as I had assumed, appear to have been related to each other and the bizarre behaviour of Time Machine was a part of this also.  One day later everything had been resolved. The AntiVirus definitions have neen downloading successfully for a couple of weeks now. The diagnostic test indicates zero problems with the System Root file/memory. Time Machine has also been reactivated as is again working perfectly.

So, Thanks to StephenB  who suggested this course of action. It has worked out well. I will also add that I mentioned to the tech support team several times that this issue is affecting quite a few people and I am pretty sure they have been working on this including the material Marc_V  has been sending through.