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What happens, if one day, the London Underground becomes too big to accomplish visiting all the stations within the opening hours? Will the FNC come to an end? How unlikely is this to happen?

It seems unlikely. Given that the record stands at 16½ hours, there is still some room for expansion. Most proposals for new lines tend to create new interchanges at existing stops in central london and then take over existing branches in the suburbs (Chelsea -Hackney was meant to take over the Wimbledon and Epping branches, for example), so a new line would not necessarily mean a large number of new stations to visit.

Extensions to the Overground or Crossrail seem more likely than extending the Underground. There is debate at the moment as to whether Crossrail 2 (formerly Chelsea - Hackney) should be built as a tube or a 'proper' railway line.

Don't forget, in 1960 the network was geographically a lot larger than it is now, and it was possible to do it in one service day.