I just had an incident like that a month and a half ago. Customer reported repeated internet outages in the morning. Lots of back and forth by phone and email, and the only conclusion I could come up with is that the ONU or router was flaky and needed to be replaced.
Nope. Ended up going on site one day. It turns out that the power bar everything was plugged into was sitting on the floor at the back of the desk in the customer's office. When they sat down first thing in the morning, they would often jostle one of the power supplies just enough to cause a restart. Moved the power bar over 2 feet to the left where feet couldn't reach it, and the problem was solved.