To determine willfulness with unfiled FBAR forms, the IRS will look at facts such as:‏

• Was the income from the foreign financial account reported on the income tax return?
• Was the box checked “Yes” or “No” at the bottom of Schedule B where the question “At any time during the tax year, did you have a financial interest in or signature authority over a financial account (such as a bank account, securities account, or brokerage account) located in a foreign country? “ is asked
• Were the bank statements for foreign financial account being sent to a U.S. address?
• Was the tax professional advised of the existence of the foreign financial account?
• Was there a valid reason for the maintenance of the account?
• Why was an account opened and maintained in a foreign country?
• What is the connection to the country where the bank account was opened and the taxpayer?
• Is the account in the name of the taxpayer or in the name of a trust or other offshore entity such as a foreign corporation?

The FBAR statute continues to run whether or not the FBAR was filed. According to the IRS the FBAR statute may be extended by consent, although there is no explicit statutory authority for this view. The SOL is based on the penalized event -- June 30 of each year passing without filing. It does not run from the date of filing a delinquent FBAR. Of course, if the delinquent FBAR is willfully false, then a statute of limitations for another crime may commence.
 
The IRS recently published a memorandum discussing the special 6 year statute of limitations rule for $5,000+ omissions of income from specified foreign financial assets enacted in FATCA which also contained Section 6038D special reporting on Form 8938.  See IRS Memorandum from Director, Examination Policy, dated 3/9/12, here. This statute extension applies to all items on the return but, upon showing of reasonable cause and not willful neglect, the extension applies only to income items associated with the failure.

The unlimited SOL applies only to the civil side of the income tax. There is no unlimited criminal SOL. And, there is no unlimited civil SOL for the FBAR. If willfulness (the FBAR analog of civil fraud) is involved, the SOL is still just 6 years.