At least six years, and possibly forever. While the government has only six years from the date the nonfiled return was due to criminally charge you with failing to file a tax return, there is no time limit for collecting taxes and assessing financial penalties for not filing. It is not until you actually do file a return that the audit time limit -- three years -- and collection time limit -- ten years -- starts to run.
As a practical matter, however, if you haven't heard from the IRS in six years, you don't need to worry too much about taxes owed on a nonfiled return. The IRS usually doesn't go after nonfilers after six years -- unless the IRS begins its investigation before the six years elapsed and you owe a large amount of taxes. After six years, the IRS frequently purges its computer files.