A UPS would only help if the hub is being hit with a power disturbance such as a black-out or brown-out. An EMC or RFI filter might help if the problem is mains-borne interference.
As it doesn’t happen at exactly the same time every night it is not likely to be something switching on and off by a timer (heating, lighting, hot water, streetlights). And why only at night? If it’s an appliance (TV, washing machine, dishwasher) that’s doing it, why doesn’t it ever happen during the day?
It could, conceivably, even be equipment at the exchange being hit with a power disturbance or RFI. I investigated a problem at an industrial site once where electronic equipment occasionally went loopy. This was traced to taxi cab radios. If it’s an external device causing the drop-out it’s going to be very difficult to trace.
By the way - it would have helped enormously if, when I first reported the issue, the BT representative had not told me that BT hubs were SUPPOSED to reboot overnight.
