OK, then I am out of guesses, time for systematic analysis.
I once had an unstable ISP and ended up making a script pinging the hosts along the traced route, so I could pinpoint the exact time and component failing at recurring intervals. This way I managed to locate a defective component in the ISP's infrastructure, much to their surprise. I suggest you do something similar. Could be that everybody had the same thought as you and this overloads (part) of the network at night.