The Educational Maintenance Allowance was introduced in Wales in 2004/05.
Nearly 7,500 of Wales' poorest sixth form students have not yet received grants designed to encourage them to stay on in school or college.
The Education Maintenance Allowance - worth up to £30 a week - can be claimed each year by pupils aged 16 to 18 who come from lower-income families.
One education union said the delay was a "disaster" and that vulnerable pupils might leave full-time education.
The assembly government insisted all those who qualify will get the grant.
It is understood that those who are still waiting for their grants will have to wait at least another month for their payments, which will be back-dated to the start of the academic year.
Students can qualify for a weekly allowance of £10, £20 or £30 depending on household income if they keep up a "satisfactory" attendance at schools or further education colleges in Wales.
It's a terrible shame to think that young people will be going without their money for so long
Philip Dixon, ATL Cymru
They can also qualify for periodic additional bonuses of £100 if agreed learning objectives are met.
Philip Dixon, director of the Association of Teachers and Lecturers Cymru (ATL) said the delay could undermine work being done to encourage youngsters to complete their education.
"This is nothing short of a disaster," he said.
"It could really put off the most vulnerable young people from entering Further Education this year. It will also undemine the positive work of the Welsh Assembly Government and clearly needs to be investigated fully.
"It's a terrible shame to think that young people will be going without their money for so long."
The Education Maintenance Allowance (EMA) Wales scheme was introduced for 16 year olds for the first time in 2004/05. In 2005/06, the scheme was extended to include 16 and 17 year olds and, in 2006/07, 18 year olds.
By the end of October, 31,930 applications for EMAs had been received for the 2008/09 academic year. Of those, 17,490 were approved and 380 rejected.
Of the 14,060 applications remaining, around 5,000 are being chased because of incomplete information on their applications and about 1,600 have other queries to be resolved regarding their applications. This leaves about 7,460 still to be assessed.
Similar delays in England have been blamed on administrative problems with contractors Liberata, who face a possible fine. But they have not been used in Wales.
Instead, the grants are administered by the Student Loan Company, but it is not yet known whether any action will be taken against them.
An assembly government spokesperson said: "Every student who has applied for an EMA will receive their payments provided their application is valid and they have attended their course.
"If the application was received two months prior to the course commencing, payment will be backdated to the start of the course.
"If the application was received after this, payment will be backdated to when the application was received."
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