Backups start failing after a week or so

What you do on Windows isn’t so clear, but because you’re talking about mounting, maybe you want this:

How To Automatically Mount NFS File System with AutoFS

Basically mount on access rather than mount at boot? If so, there’s lots more information on the Internet.

I don’t personally use this and I don’t know how common it is, but I don’t recall hearing it hurts Duplicati…
Another thing that people can do is to use Duplicati scripting options to mount, do backup, then unmount.
I suppose one consideration in all this is which solution gives the desired ability to deal with mount errors.

As a test, you can try changing Settings for Usage statistics:

Setting this to None will disable reporting usage statistics at all.

which looks like it will disable upload. Does it always fail (maybe once per backup) or only sometimes?
What OS is this? This error looks like one that’s begun due to mono, OS, and Let’s Encrypt certificates:

Http send report errors / duplicati-monitoring has one of the better workaround lists, but there are others.