Tory MPs fear their party risks a “bashing” from older voters if the Prime Minister presses ahead with axing the flagship pledge, in order to cut the growing bill for pensioner benefits.
There is also disquiet that the handling of the row has been a “car crash”, after Ms May struggled under questioning at the Commons despatch box.
Meanwhile, the National Pensioners Convention warned that the stance of all parties on the triple lock would be a “litmus test for the grey vote” on election day.
Significantly, both Labour and the Liberal Democrats have pledged to keep the guarantee that state pensions will rise in line with inflation, average earnings or by 2.5 per cent – whichever is the higher.
“Any party that says it is getting rid of the triple lock, well, that will play badly. It is a litmus test for the grey vote,” said Jan Shortt, the National Pensioners Convention general secretary told The Independent.
The controversy deepened after the SNP leader in Westminster, Angus Robertson, clearly discomforted Ms May in the last Prime Minister’s Questions before the general election.
Twice, Mr Robertson asked what he called “a pretty simple yes-no question” – whether the triple lock would be kept if the Conservatives win on 8 June.
But in reply a stuttering Ms May said only that “under a Conservative Government, pensioner incomes would continue to increase”.
Behind the scenes, the Prime Minister is believed to be weighing up whether the huge Tory poll lead gives her the freedom to dump the expensive triple lock pledge she inherited – as austerity continues into the next decade.
A Conservative source told The Independent that most Tory MPs believed it will go, adding: “There’s an election, so of course they will have to support it publicly, but there is a lot of unease about it.
“Look at the age profile of our voters, with so many of them pensioners. MPs fear we will take a bashing over it.
“Also, the handling of it has been a car crash, as you saw at prime minister’s questions. The PM didn’t seem to know how to answer questions about the triple lock.”
One senior MP, Sir Desmond Swayne, David Cameron’s former parliamentary aide, said: “We should keep it. We need to keep it for at least another Parliament and then review it.
“Some people would argue the problem has been solved – that many retired people are now better off and are no longer falling behind – but I don’t think we are there yet.”
However, Sir Desmond suggested the issue was less controversial with his Hampshire constituents than it appeared to be at Westminster – and far less controversial than 0.7 per cent foreign aid pledge, which will be retained.
Ms Shortt, for the Convention, added: “State pensions have still not made up what they lost when Margaret Thatcher broke the link with earnings in 1980.
“There is an idea that the triple lock has done its job, but it has not. The state pension is still inadequate and lower than if the link had not been broken.”
And Caroline Abrahams, charity director at Age UK, said: “The triple lock provides an essential safety net for millions of pensioners, particularly the 1.9 million currently living in poverty and struggling to afford the basics.”
However, support for dropping the triple lock came from Ros Altmann, the former head of Saga and a former Conservative pensions minister, who tweeted: “State pension triple lock isn’t working properly. It's illogical and leaves out poorest oldest pensioners.”
Some Conservatives still believe Ms May will decide to stand by the triple lock, when the party’s election manifesto is unveiled on 8 May.
They argue it is likely to be a cost-free promise for the next few years, because of official predictions that wages and prices will rise at something close to 2.5 per cent in any case.
Last month, Chancellor Philip Hammond promised the triple lock would remain in place until the next planned general election in 2020, but would be reviewed ahead of that date.
But, in calling the snap election for 8 June, the Prime Minister is known to be keen to shed herself of some policy commitments made by Mr Cameron and George Osborne.