You need to keep seven years' records for tax purposes, but there is no such thing as a statute of limitations when tax returns haven't been filed.

Bottom line rule is to always file, even if it's wrong or incomplete or you can't pay. At least that starts the clock running, otherwise it doesn't happen. When I was still practicing law we had the IRS make an appearance in a case requiring the filing of tax returns that were 12 and 13 years old that they said my client hadn't filed. Luckily the guy had them (either the IRS or UPS had lost them) and was able to produce his copies.