Initial recation is that it is the ISP dropping the connection and re-establishing.
I'm with PlusNet (part of BT these days) and every few days they go through a process of breaking / making the connection several times. I think they do this to assit in determining the service level that can be supported.
Do you know if the router re-boots entirely or does the router stay powered up throughout? If the router re-boots, it might suggest that there is an appliance that momentarily sucks power in your property at 06:40 (e.g. Central Heating kicking in).