BBC links to a a study published by the Fabian Society, making the point that "Labour is too weak to win, and too strong to die". By this they mean that Labour has, basically, a very large number of safe seats with large majorities. So if it loses votes, it simply has a lower majority in each of its seats, with relatively few loses ("too strong to die"). But it is also "too weak to win", in their words, since a small swing towards it just raises its majority in seats it already will win.
Figure 4 contains the key data, all using national shares of the vote.
Columns 1 and 2 show what happens if Lab get 20% of the vote, a very very low share, Con 45 and the others are split. Lab doesn't win, but still gets 140 seats (currently it has 232). Columns 3 and 4 show what happens if the Libs get up to the same as Labour, at 20. Note that Labour hardly suffers: indeed it wins more seats and the Libs get hardlly any more. Columns 5 and 6 show the same.
The BBC website summarises this nicely:
Yet the figures suggest that despite the current low standing, a large majority of Labour MPs would be re-elected.
That's because a lot of them are in safe seats.
An interesting feature of recent British electoral politics is that the number of safe seats has increased whereas the number of marginal seats has fallen.
In 1992, 169 of the seats in Great Britain were won with majorities under 10% - a common definition of a marginal seat. In 2015, that number was just 119. And only 49 of those were won by Labour.
On the other hand, the number of very safe seats has increased. In 1992, there were 155 seats won with majorities above 30%. In 2015, there were 223.It continues:
A further interesting quirk of British elections is that the extremely safe seats in the country tend to be Labour seats, even when it loses the national vote.
The 11 safest seats in the country are all Labour - as are 17 of the safest 20.
That doesn't mean those constituencies could never elect an MP from another party. In 2015, Labour lost some very safe seats in Scotland as a result of the SNP landslide. But it does mean that for many Labour MPs, even the current polls shouldn't cause them too many worries about their own futures.
This trend became even more acute in 2015.
The Conservatives pulled off their surprise victory by winning votes just where they needed them, such as in Liberal Democrat-held seats in the south west of England - which is now almost entirely blue.
On the other hand, Labour piled up lots of extra votes in seats it already held comfortably.So nationally their vote share went up even as they lost seats overall.
I think this also answers another question: why didn't Lab MPs, who don't like Mr Corbyn very much by all accounts, but cannot get rid of him, try to start another party? Part of the answer is that a core group of them, on these maths at least, don't have to worry about their seats.