ALL DATABASE backups failing with Error 41 ( Network Connection timeout )

Client is simply taking too long to generate backup stream:

Backup starts at 5:59:40.
Only at 6:07:27 does it start to evaluate local drive letters.
At 6:15:19 client is ready to 'START BACKUP'.

By this time, the Client Read Timeout on the media server has been exceeded and we see this message:

<16> dtcp_read: TCP - failure: recv socket (648) (TCP 10054: Connection reset by peer)

As per my 2 previous posts - you need to see what is happening on the client when the backup kicks off:

This says to me that the client is trying to generate data stream but has not been able to do so within the 5 minute timeout period. You can increase the timeout on the media server, but better to fix the problem on the client.

You need to see what is happening on the client when the backup is started. Check AV software: Is it scanning each file? Is it preventing files from being sent?