Research by pollster BMG for Huffington Post found that 54 per cent said Corbyn should stay, regardless of the next election result.
Just one in eight Labour supporters said he should step down if Labour loses.
By contrast, less than one in four members of the general public said Corbyn should be allowed to stay on.
Corbyn expanded his mandate in the recent leadership contest against Owen Smith, but polling by Survation this week put the Conservatives on track for a majority of more than 70 seats in the House of Commons.
And the figures from BMG also show limited supported for an early general election – only one in three said May should head to the polls before 2020.
And Conservatives where the least likely to support an early vote, with just 17 per cent supporting the suggestion.
By contrast almost 60 per cent of Labour supporters backed a ballot ahead of the next scheduled election.
BMG head of polling and research director Michael Turner said: “What is clear is that if Theresa May does call a General Election in 2017, many of Jeremy’s supporters might not expect him to deliver electoral victory, leaving open the prospect of his leadership continuing indefinitely”.