For a separatist or any city to be successful, it needs to bring in money from other cities. Tourism is the most direct way I can think of. Las Vegas is similar to California City - a city in the middle of the desert, but is viable because of tourism. But tourism is very boom/bust.

The better option is having a company/industry located in or close to that city (e.g. money from all over the US goes to Apple, which it distributes to its employees who spend money in the Cupertino, San Francisco, etc.) BUT this isn't fool proof -- look at Detroit.