How often does a 501c3 have to be audited?

I don't think 26 USC Section 501 (c) (3) (http://www.law.cornell.edu/uscode/text/26/501), or the pursuant regulations, contain auditing rules. Check the non-profit corporation code for the state in which the organization is organized.

According to this site:

http://www.startnonprofitorganization.com/audit-requirements-nonprofits

Any org receiving $500K/yr in federal funding must have an annual audit, and also depending on the state if the org exceeds a certain threshold of annual revenues it must have an annual audit. So those are the rules, but my advice is that any organization with an operating budget of $200K or more should have annual audits even if not required by law. There are too many opportunities for malfeasance, or the appearance of malfeasance, which can destroy the organization.

... Any org receiving $500K/yr in federal funding must have an annual audit,...

Of course not all 501 (c)(3) organizations receive funding from the federal government; probably most get all funding from private donors.