It seems the IRS can continue auditing as long as the statute of limitations has not expired. I base this on this quote from this irs.gov article for small businesses and self-employed individuals:
If an audit is not resolved, we may request extending the statute of limitations for assessment tax. The statute of limitations limits the time allowed to assess additional tax.
And on disagreeing to extend the deadline on the statute of limitations when it approaches:
You don’t have to agree to extend the statute of limitations date. However if you don’t agree, the auditor will be forced to make a determination based upon the information provided.
The American Bar Association has an article on the statute of limitations:
The IRS Typically Has Three Years. The overarching federal tax statute of limitations runs three years after you file your tax return. If your tax return is due April 15, but you file early, the statute runs exactly three years after the due date, not the filing date. If you get an extension to October 15, your three years runs from then. On the other hand, if you file late and do not have an extension, the statute runs three years following your actual (late) filing date. There are many exceptions discussed below that give the IRS six years or longer, however.
Six Years for Large Understatements of Income. The statute of limitations is six years if your return includes a “substantial understatement of income.” Generally, this means that you have left off more than 25 percent of your gross income. Suppose that you earned $200,000 but only reported $140,000. Given that you omitted more than 25 percent, you can be audited for up to six years. Maybe this understatement was unintentional or you reported in reliance on a good argument that the extra $60,000 was not your income. The six-year statute applies, but be aware that the IRS could argue that your $60,000 omission was fraudulent. If so, the IRS gets an unlimited number of years to audit. What about not an omission of income, but overstated deductions on your return? The six-year statute of limitations does not apply if the underpayment of tax was due to the overstatement of deductions or credits.
It then elaborates on that, and finally mentions that it can last indefinitely, in specific cases (emphasis at the end is mine):
- IRS Form 5471. Ownership of part of a foreign corporation can trigger extra reporting, including filing an IRS Form 5471. It is an understatement to say that this form is important. Failing to file it means penalties, generally $10,000 per form. A separate penalty can apply to each Form 5471 filed late, incompletely, or inaccurately. This penalty can apply even if no tax is due on the whole tax return. That is harsh, but the rule about the statute of limitations is even more harsh: If you fail to file a required Form 5471, your entire tax return remains open for audit indefinitely.
Another reason in the article (I skipped a few paragraphs of elaboration)
- No Return or Fraudulent Return. What if you never file a return or file a fraudulent one? The IRS has no time limit if you never file a return or if it can prove civil or criminal fraud. If you file a return, can the IRS ever claim that your return didn’t count so that the statute of limitations never starts to run? The answer is “yes.” If you don’t sign your return, the IRS does not consider it a valid tax return. That means the three years can never start to run.
And further down, the IRS may ask for an extension:
Extending the Statute. The IRS typically must examine a tax return within three years, unless one of the many exceptions discussed here applies, but the IRS does track the three-year statute as its main limitation. Frequently, the IRS says that it needs more time to audit.
The IRS may contact you about two-and-a-half years after you file, asking you to sign a form to extend the statute of limitations. It can be tempting to relish your power and refuse, as some taxpayers do; however, doing so in this context is often a mistake. It usually prompts the IRS to send a notice assessing extra taxes, without taking the time to thoroughly review your explanation of why you do not owe more. The IRS may make unfavorable assumptions. Thus, most tax advisers tell clients to agree to the requested extension.