Both organisations have been asked for further information before a final decision is made.
CNZ chief executive Stephen Wainwright said yesterday "several things" led to the decision.
"They threw their hats in the ring, but what we're looking for is organisations to play a leadership role in their art forms. What we're saying to the Fortune and Southern Sinfonia is, 'You gave it your best shot, but we're not confident at the moment that you've made a compelling case."
'The criteria were strong governance, management, artistic management and direction, he said.
Twenty-two organisations were selected for the new programme, while 10 organisations, including the Fortune and sinfonia, were asked to provide further information "to help assess their fit with the programme", Mr Wainwright said.
Recurrent funding would be maintained for next year and the 10 organisations would be advised of outcomes next September.
Fortune Theatre Trust chairman Peter Brown said he was not surprised by the decision.
"We had been resigned to 'maybe' status. We would have liked to have got a `yes' from the outset, but it's not the end of the story. That long-term funding is the Fortune's to lose and we're very optimistic.
"This now presents us with an opportunity to prove to CNZ that we are worthy of the support we receive from them. We feel we're well on the way to achieving that, with the appointment of a new general manager and artistic director, which was geared towards making the Fortune a leadership organisation."
However, Southern Sinfonia manager Philippa Harris said the decision was "disappointing and frustrating".
"It's very frustrating. We thought we ticked all the boxes, but apparently we don't," she said yesterday. "It's disappointing, because we are it as far as orchestral music in the south of the South Island is concerned. For a small investment, they get a huge return.
"Now, we've got to go through a rather long process and there's no way of knowing what the decision will be until September next year."
Mr Wainwright said recent management changes at the Fortune were "a factor" in the decision.
"There has been a lot of transition, especially at the Fortune, and we're interested to see what that will mean. We have to sit down and have a proper discussion with them.
"We weren't convinced of the sinfonia's ability to deliver to those keys areas and we didn't find their case compelling. They do a hell of a lot of good, but it's a dilemma in a country the size of New Zealand how many organisations you can look to to play a key leadership role."
The only two South Island organisations to be accepted to the leadership programme were the Christchurch-based Physics Room and Court Theatre. However, Mr Wainwright denied there was "a population-based formula going on".
"We know arts organisations play an important part in the communities in which they reside and we're mindful people in Otago and Southland should have access to quality arts."
If the Fortune and sinfonia fail to meet the leadership programme criteria, they may still qualify for the arts development investment programme, which offers funding from six months to two years for organisations not fulfilling a key role.
• The 22 organisations confirmed in the leadership programme yesterday were the Auckland Festival Trust, Auckland Philharmonia Orchestra, Auckland Theatre Company, BATS Theatre, Black Grace, Centrepoint Theatre, Chamber Music New Zealand, Dance Aotearoa New Zealand, Massive Company, Capital E National Theatre for Children and Wellington Children's Festival, New Zealand Book Council, New Zealand International Arts Festival, NBR New Zealand Opera, New Zealand String Quartet, Objectspace, Playmarket, Taki Rua Productions, Tautai Contemporary Pacific Arts Trust, The Court Theatre, The Physics Room, Toi Ma-ori Aotearoa and Touch Compass Dance Trust.
