Lecturers vote on Thursday on whether to uphold a boycott of two Israeli universities accused of complicity in anti-Palestinian policies.
Many AUT members complained about the first vote
The Association of University Teachers decided last month to sever ties with Bar-Ilan and Haifa universities, which deny the allegations.
But another meeting is being held, in London, after some members complained the original debate had been cut short.
The vote caused controversy among academics and others around the world.
Haifa is accused of mistreating politics lecturer Ilan Pappe for defending a graduate student's research into controversial areas of Israeli history.
It denies this and has threatened legal action.
Bar-Ilan is alleged to have helped with degree programmes at a college in a settlement in the West Bank, which it says is autonomous.
The AUT council was reconvened after more than 25 members complained about the previous vote.
Jon Pike, a senior philosophy lecturer at the UK's Open University, said 80% of members nationwide were against the boycott.
The pressure for re-opening the debate had come "from below", he added.
However, Sue Blackwell, an English lecturer from Birmingham University who proposed the boycotts, said she feared a "stitch-up" by the union's executive.
She accused opponents of "demonising and discrediting the idea of boycott and boycott activists in the UK and beyond".
Ms Blackwell has said she expects to lose the vote, which is taking place in London behind closed doors.
AUT members are expected to make their decision by 1600 BST on Thursday but it may not be published officially straight away.
The debate has raised passions among academics and others around the world, with organisations speaking out for and against the idea of a boycott and often denouncing each other's viewpoints.
Among the latest, for example, the Palestinian Campaign for the Academic and Cultural Boycott of Israel, based in Ramallah, said it also expected the boycotts to be revoked, in a climate of "vilification and misinformation".
But it said the process of awareness-building launched in preparation for the AUT's initial meeting "will persist and can only grow".
The American Association for the Advancement of Science on the other hand urged an "immediate repeal" of the boycotts.
"Multi-national research collaboration should never be compromised to advance a political agenda," it said.
Natfhe - the union which represents most academics at the newer universities, most of which were once polytechnics - has been presented with an emergency motion in support of the boycott.
A decision on whether to debate this at its annual conference next Monday will be taken by a steering committee on Friday night.