This is important - A lot of the info on the Internet about this is out of date. They changed the rule on this recently.
(Recently = effective December 18, 2013)
This web page summarizes the details. http://www.clm.com/publication.cfm?ID=489
The short version is that if a patent holder pays both the maintenance fee and a late fee, they can revive a lapsed patent any time at all, until the 20-years-from-filing date on which the patent would have expired anyway.
(This 20-year limit can also be changed by a terminal disclaimer, and by PTE patent term extension or PTA patent term adjustment, and there's a different 17-years-from-issue expiration date for patents filed before June 8, 1995. But, that's a separate story; see http://www.uspto.gov/patents/law/patent_term_calculator.jsp#heading-3 for details.)
Zombie Patents: Stronger Than Ever
May 14, 2014
by John M. Griem, Jr. and Theodore Y. McDonough
Until recently, a patent which expired for failure to pay a maintenance fee could only be revived as unintentionally abandoned within 24 months of the date the maintenance fee was due. While a petition to revive an unavoidably abandoned patent could be made at any time after the patent’s expiration, the “unavoidable” standard was almost impossible to meet.
Recent changes to Title 35 of the U.S. Code effected by the Patent Law Treaties Implementation Act of 2012, Pub. L. No. 112-211, 126 Stat. 1527, eliminate the unavoidable standard and remove the 24-month time limit to reinstate an unintentionally abandoned patent. Now, any patent which has expired for failure to pay a maintenance fee can be revived, at any time, upon a statement that the delay in paying the maintenance fee was unintentional. 35 U.S.C. § 41(c)(1). Similarly, any patent application that has gone abandoned for an unintentional failure to file a timely response can be revived at any time. 35 U.S.C. § 27; 37 C.F.R. 1.137.
Hope this helps!