The future of the Scottish Anti-Bullying Network, similarly based at Edinburgh University, is also in doubt after its bid to win a five-year contract to develop anti-bullying practice was rejected.
The Executive said that none of the tenders for the anti-bullying contract would develop the service in the way it wanted and that the contract would be put out again in the autumn.
The Anti-Bullying Network's bid was supported by a number of organisations, including Childline, Barnardo's, Children in Scotland and LGBT Youth Scotland.
Current funding for the anti-bullying network is to be extended for a further eight months to ensure that no momentum is lost.
A spokeswoman for the Executive said: "We want to see the service extended beyond the school gate and include things like out-of-school activities in community settings, places where children are just as likely to be bullied."
The work of the ethos network would be carried on through a range of initiatives, including Solutions Orientated Schools in Moray (ScotlandPlus 2-3), leadership programmes such as Columba 1400, health-promoting schools and integrated community schools.
Andrew Mellor, manager of both the ethos network and the Anti-bullying network, said: "To put it in a nutshell, they said the ethos network had been a victim of its own success in that ethos is firmly on the agenda and it is included within HMIE's How Good Is Our School? guidance. The inspectorate reckons that the ethos of schools is very important and other organisations are constantly talking about ethos as well. So the Executive's thinking is that there is not a need for the network any more."
Mr Mellor's own view is that schools still want the services of the ethos network. "Practice can always improve," he commented.
The ethos network, which has 2,000 members, was set up in 1995 and the anti-bullying network in 1999. Both are directed by Pamela Munn, dean of education at Edinburgh University, and recognised as one of the foremost authorities on ethos, discipline and bullying.
Brian Boyd, of Strathclyde University's education faculty, called the decision on the ethos network "reprehensible", particularly when the Executive was promoting the idea of communities of innovation through its Curriculum for Excellence. "Scotland has led the way in ethos indicators and the network has sustained a really high level of engagement," Professor Boyd said.
The Headteachers' Association of Scotland has written to the Scottish Executive Education Department, expressing its disappointment at the decision. "It cost only pound;100,000 a year - it is not as if we were talking about megabucks," Bill McGregor, the association's general secretary, said.
Ronnie Smith, general secretary of the Educational Institute of Scotland, said: "If the SEED is going to stop spending money on these initiatives, is the money being reallocated elsewhere or is this part of its contribution to the Scottish Executive-wide budget clampdown?"