Sounds to me like you could have the start of a firmware problem, this will get worse through time, from what i remember this can be caused by the router trying to do an online firmware upgrade but no ...
The Livebox was made by inventel but Inventel was Taken over by Thompson, the makers of the speedtouch series modems, also as a point of interest they also make the BT home hub.
but don't expext to f ...