hmm...
If Rhisiart has the 2.53 GHz listed in the signature, then that can't download Mojave, at least not using the normal method. (it would be limited to the latest macOS that it can run)
@Rhisiart - Are you saying that Ethernet (even with the Wifi card turned off) ALSO drops off?
Yes.
Is there any improvement if you restart your router?
No.
Is the dropout always at the same point in the download?
Not sure. Possibly. As far as surfing the web is concerned these intermittent connection losses are tolerable, but it's real pain when trying to do a large download as you can well imagine.
Can you restart your mini, then (with ethernet only connected) start the Mojave download? Do not use any other apps, just let the download continue without doing any other task. (and, also, don't use the internet through your router on another device, until you can see that the mini isn't going to be successful)
As it happens, I managed to get a window of Internet connectivity normality yesterday. Lo and behold I was able to download Mojave and have a done a reinstall. Sadly the Mini will still not restart although it does now wake up from sleep mode.
I don't know what else to do. Perhaps I'll run Diskwarror again.