Their refusal comes despite the government telling local authorities how much money they will get from the new fund for the next three years.
In October, the £335m Graduate Leader Fund replaced the Transformation Fund, which was left severely underspent due to its short-term nature and complicated application process.
The National Day Nurseries Association (NDNA) said some councils are telling its members funding could only be promised for a year at a time.
"The Graduate Leader Fund is a long-term investment and funding tables sent to local authorities indicate how much they will get over three years," said Purnima Tanuku, chief executive of the NDNA.
"Some councils are saying they can only commit for one year, which is total nonsense, and we are telling members to go back and tell them so. You can't commit to a qualification with that kind of funding."
Rahim Ahmed, programme co-ordinator for Early Years Professional Status at qualification provider Best Practice Network, said: "The government has committed to the fund until 2011 so authorities saying they can only commit for a year goes against the fundamental direction of this funding."
According to the NDNA, some authorities may be reluctant to commit because they want to be sure the person being funded will complete their qualification. It is not known if workers will have to re-apply for the money every year of their course.
