The Liberal Democrat party: a dead parrot or a phoenix? Political roadkill or cockroach surviving a nuclear winter? Lib Dems themselves don’t quite know. Ask a local campaigner, and the answer will be rather optimistic. The party has done well in this year’s byelections, and the membership, galvanised by Brexit, has recently risen to almost 100,000. Crucially, the memory of the toxic coalition years appears to be fading: the disheartening phrase “tuition fees”, campaigners say, is no longer heard so often on doorsteps.

But staff at its London headquarters are frustrated, not least as the party is now planning to make a quarter of them redundant to save money. They are all too aware of the double opportunity the party has been handed: Britain’s political centre, along with some 16 million remain voters. Here is a chance – one, surely, in several lifetimes – for the party to take a big leap forward. Yet it struggles to rise above 10% in the polls, and its MPs get little airtime. So why can’t the Lib Dems seize the moment?

It may not be entirely the fault of the current team. Traditional Lib Dem voters don’t necessarily love Europe, says Andrew Russell at the University of Liverpool, and the party’s heartlands are mostly in leave areas, meaning its anti-Brexit message has an uneasy relationship with the existing base. The party may have had the chance to emerge gloriously as a new political force, but many feel this chance was used (and blown) by Nick Clegg – now, symbolically perhaps, fleeing to a new career in Silicon Valley. Voters are now familiar with the Lib Dems, and cannot see them as something radical or exciting. Then there is the perennial problem of being one of the minor parties, which always struggle to get much media attention between election cycles.

But the party is missing some tricks. One former staffer complains that the party, famed for its niceness and for wearing socks with sandals, has failed to position itself in “the angry space” the times demand. Its new slogan – “demand better” – is a start, but the party isn’t nearly strong enough on Brexit: strategists get bogged down in the uncertain technicalities of a second referendum, rather than matching the insouciance of their Brexiteer opponents. They could also do better at marrying their national message with their local ones: making it clear, for example, that it would serve fishermen and farmers to stay in Europe, and pointing out how Brexit might affect the money available to local services.

But it is a party’s leader who really decides its fate. Remainers – including the 700,000 people who marched in London last month – are galvanised, and crying out for someone to represent them, but Vince Cable is not the person to do it. He may please the party membership – who agree more with him than they did with Tim Farron or Clegg – but he is not charismatic enough to capture imaginations outside this sphere. His image is that of an ageing fusspot, obsessing over party process while bungling more important matters (unforgivably, Cable and Farron failed to turn up to oppose the government in a key Brexit vote in July that passed with a majority of three). Someone else should lead the party.

The trouble is finding them. Emerging talents such as Jo Swinson and Layla Moran have been tipped for the leadership, but party members say they have yet to act on any ambitions they may have: “If they want it,” one says, “they must seize it.” The hope that outside candidates might come forward hasn’t yet yielded much either. The Lib Dems recently announced a rule shake-up so that people other than the party’s 12 MPs could run for leader, but the most keenly anticipated name, Gina Miller; quickly ruled it out.

Cable, to be fair, doesn’t seem to be standing very firmly in anyone’s way. He may have announced intentions to stay in post until Brexit is “resolved”, but members tell me this is partly because no one else is currently in contention, and he is “trying to create the conditions for someone to come forward”. “He has been quite mature about the fact his job is to pave the way for the next person,” they say, and will probably step down when they emerge. In any case, if he does not, “the knives will be out”. Until this happens, the party is unlikely to take the leap forward it hopes for.

The Lib Dems are good at coping in hostile environments. They recovered from their low moments in the 1950s, when they held just six seats; they recovered from their “dead parrot” years under Thatcher; and they will recover from their current predicament. But now they must show they can cope with an opportunity too.

• Martha Gill is a freelance political journalist and former lobby correspondent. She has worked as a staffer at the Economist and the New Statesman