If I understood correctly the OP has the HDD attached to the NDX USB socket, and not networked at all(?)
And the iPad control is wifi from iPad to internet switch to NDX.
If that is correct, the issue might be the internet access point /wireless router somehow failing, rather than the internet provider’s actual internet service, breaking the wifi link from the control app to NDX.
Gramophone, i) does that fit with what you are doing and what seems to happen? and ii) have you tried controlling the NDX with its own remote and the inbuilt screen when the internet is down as you put it?
But if that is the case, I am unclear why the wireless router is failing - usually internet problems are nothing to do with the wifi side and don’t affect it, so making me wonder if all the problems are actually a faulty wireless router.