I am going to guess here and i suspect Eurosport will have been uninterrupted and this fault only happened at the bbc because someone there pulled the wrong plug out at source?
It is really not often someone pulling a plug, although it is not impossible.
If it was a satellite uplink on site providing the feed back to the BBC Network, then that could have had any form of equipment failure, power breakers tripping, the high power feed into the dish failing - the signal is carried on waveguide which can have issues, the satellite being illuminated by someone else, wiping out your signal, or something on site changing blocking the path to the satellite.
The satellite could have problems, the downlink could have a fault, the lines from there to Network could too.
It is an endless list of "what ifs" that you deal with, and ultimately you can try to engineer separate paths that have no common point of failure.
One common point that is very reliable, but is not 100% is BT Tower. That had a major failure during the X Factor from Fountain Studios a few years ago. That affected the main via fibre and via Tower to ITV, but the microwave backup (via Crystal Palace and then to BBC TVC) was then fed by circuits to ITV via BT Tower too.
All major points are generally robust, but not totally.