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Virgin Media Warns UK Broadband Users Not to Switch Routers Off at Night - ISPreview UK
(www.ispreview.co.uk)
This is a most excellent place for technology news and articles.
The malware argument is a bit weak, if your router is vulnerable to something it'll likely be found and pwnd in a matter of minutes, so turning it off a night won't really save you. And once a patch is released, it'll be reverse engineered in a few hours/days, so ideally you want patches as soon as they are released.
Using your own device is usually a good idea anyway, telco stuff is usually pretty mediocre. And as soon as your device is slightly custom, it becomes a less valuable target.
It's much more than just a bit weak, unless you are somehow continuously monitoring it, so yeah, in most end-user scenarios, it would hardly make a difference to keep it on, even if there were no updates.