Same time every night? Or alternately, does it happen at the same time past the hour? If it's somewhat predictable, do you have the capacity to hook your computer straight to the modem taking the router out of the equation?
Years ago I had a router that would boot me on a timetable. I believe it was every 6 hours on the dot, from the time I reset the router. If memory serves it was to do with how it was doing DHCP, switching to a static IP solved that particular issue. Not saying that would apply in your situation, the point is consumer grade routers in my experience can have some odd behaviors.
Wiley.