The course had just received a glowing OFSTED report.
But TTA limits - imposed when it failed an earlier inspection on its quality assurance - mean it can take only half the number of students it says it needs to survive.
Sixty students have already applied for the 25 places on next year's course. But the university council is expected next week to rubberstamp the education department's request to close the course.
It will make it the first successful primary course to close in recent years. The Open University has just closed its primary course after failing an inspection but most casualties have been among hard-to-recruit secondary courses.
Sussex vice-chancellor Professor Alasdair Smith said: "Our programme is too small and TTA rules mean it will stay too small. Numbers were cut in 1996 and it doesn't matter how well we do subsequently, we can only crawl back up to viability."
Changes in regulations forced the rewriting of courses, and schools, already coping with Government initiatives such as the literacy hour, were increasingly reluctant partners in training.
"We are very disappointed," Professor Smith said. "All our PGCE courses are based on very strong links to schools in the region. We don't like to see part of that provision close."
Sussex also blames the burden of repeated OFSTED inspections. The Universities Council for the Education of Teachers estimates the cost of inspections to providers at an average Pounds 35,000 per year. A joint OFSTEDUCET working party will examine the issue next year.