Although the policy was not in the Labour/NZ First Coalition agreement, Labour's supply and confidence agreement with the Greens said the Government would: "make tertiary education more affordable for students and reduce the number of students living in financial hardship".
Victoria Postgraduate Student's Association president Elizabeth Olsen told MPs that post-graduate students' wellbeing was being affected because of financial hardship.
"We expect post-graduate students to weather short-term poverty in the expectation that they will earn more than the average [student] after they have received their degrees.
"But we don't consider the potential negative consequences of this poverty," she said.
She said the number of students who would need the allowance was relatively small.
During the last year the allowance was offered, in 2012, 5000 students enrolled in a master's programme – just 30 per cent of whom received a student allowance.
In the same year, there were 920 PhD students across New Zealand and only 180 received a student loan.
"The actual number of people who need this support is small, but they shouldn't be overlooked," Olsen said.
She said restoring the allowance was in line with the objectives of the Government's wellbeing budget.
Despite this, there was no mention of it in May's budget.
A spokesman for Education Minister Chris Hipkins would not explicitly say if it was still the Government's intention to reinstate the allowance.
"As with all spending decisions it will be considered in the context of the next Budget."