The body that administers the third level grant system has said 1,500 more students are due to be paid their money this week.
The City of Dublin VEC, which oversees the Student Universal Support Ireland (SUSI) system, also said that 3,000 students had still not provided their bank details or college registration confirmation, which was delaying their payments.
It comes as the Union of Students in Ireland said that many students were relying on food donations to keep going, while waiting for their maintenance grants.
USI President John Logue said food boxes had been set up in student union offices in college campuses around the country.
Speaking on RTÉ’s the News at One, Jacinta Stewart of the City of Dublin VEC said 27,606 applicants have already been awarded grants.
She said that some of the delay was down to the students themselves.
She said: "Most of them have in fact supplied their bank detail information to us, but there are about 3,000 whom we still have to get.
"But we've been making awards right up until the last few days, so some of those are very recent."
An external review of the new SUSI system is due to be carried out.
Ms Stewart said the City of Dublin VEC would look at everything it was doing:
She said: "Every new process needs to be examined once it's completed to ensure you can improve delivery."
Ms Stewart said that from this year, the CAO will provide details of where a student will be attending college and what course they are doing, which will remove the need for confirmation from the colleges.
She also said that SUSI had received 10,000 new applications after the closing date of 31 August.
The USI has said that many third level students are struggling to keep going and food boxes are one way of helping those still waiting on their grants.
Speaking on RTÉ's Morning Ireland, Mr Logue said the situation was now a crisis.
He said: "These are people who are desperately negotiating over Christmas with their landlords, pleading with them not to evict them from their student housing.
"Food boxes have been set up now in students unions across the country. This is the situation we are at in colleges across the country. This is an absolute crisis.
"I don't think the minister has fully acknowledged how deep it is, and these people have gone four months without any payment."
A spokesperson for the Minister for Education has told RTÉ they are extremely concerned about any students facing hardship.
She declined to comment on reports that student unions are assisting some students with food items, but did say that the Higher Education Authority operates a student assistance fund to which students can apply for help.
Last year, 11,000 students accessed the fund.