20-Year Prospect
It'd be lovely to say Doctors Without Borders won't exist in twenty years; that all the world's leaders will have a big conference and decide to stop killing each other, stop killing each other's people, and research cures for all the most dangerous diseases in the world. Dare to dream, right?
Back in reality (that time and place from which you're currently reading this), we're going to have wars, and impoverished nations, and terrible diseases for the foreseeable future. It's hard to believe Doctors Without Borders will cease to function so long as those things are still around.
That said, MSF needs to continually secure funding, and they prefer to receive that funding via donations rather than political subsidies (source). Remaining independent of any official political, economic, or religious views allows them to go where help is needed, no questions asked.
Could the ability to avoid political funding change in the next twenty years? Sure it could. But we're guessing the recognized nobility and importance of this career will be enough to keep it running smoothly for many, many years to come.