Maggie Cunningham said the 500,000 viewers the Gaelic channel attracts each week will fall away unless it finds inventive ways of making new attractive programmes.
The former head of BBC Scotland programmes, who took her new role in July, said it was unlikely to win extra funds from the BBC or the Scottish Government.
Her comments came as BBC Alba unveiled its new autumn schedule, which features a mix of sport, news, music and documentaries.
It includes a new documentary about Linda Norgrove, the Scottish aid worker who died during a failed US rescue attempt in 2010 following her kidnap by the Taliban in Afghanistan.
Ms Cunningham said BBC Alba, which is jointly run by MG Alba and the BBC and became available on Freeview last year, needs to look for new resources and partnerships to grow the scale of its programming.
She said the channel's current viewing figures were a very solid platform.
Ms Cunningham added: "Success always brings its own challenge, and I think the biggest single challenge we face at BBC Alba moving ahead is resource: how are we going to have enough originations, enough new and interesting content to keep our audiences onside?
"We are already just beginning to see a little bit of audience fatigue, but we have great goodwill, we have high audience approval in our core Gaelic speakers, and in Scotland, and we have had a lot of recognition of the quality of MG Alba, but it is going to be very hard to hold that audience over the next four years.
"I am not naive enough to think we can just go out there with a begging bowl. I think we have to be a lot more subtle than that, much more inventive in how we source new material. We have got to continue to exploit our partnerships as well as we can.
"We will talk to our colleagues in minority languages in other places and countries to understand what they are doing and how we can learn from them."
Ms Cunningham compared the channel to whisky, adding it will get better with age.
She said: "I am optimistic that we can continue to find inventive ways to keep the audience onside."
There are hopes the documentary, made by MacTV, about Linda Norgrove will be shown on other networks after its BBC Alba screening.
Ms Norgrove's parents, from Lewis, visit Afghanistan in Lorgan Linda: Linda's Story, directed by Douglas Campbell.
It follows John and Lorna Norgrove from the time after the death of their daughter to setting up the foundation named after her, which carries out humanitarian work in Afghanistan.
Mr Campbell said: "For Linda, it was her passion, her vocation, to help alleviate suffering and help people in difficult part of the world, and for John and Lorna I think this was a cathartic process."
There will also be live Scotland women's international football, weekly SPL games and live coverage of some Glasgow and Edinburgh Pro12 rugby matches.
l ALEX Salmond is to meet with the BBC's new director-general George Entwistle next week to discuss controversial plans to redeploy staff at its Gaelic service.
It plans to use journalists working for Gaelic TV and radio to cover for cuts in senior editorial staff in the English service in Inverness. Mr Salmond said it would put BBC Radio nan Gàidheal and BBC Alba in "a very serious position indeed".
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