I think we're in a recession until real per capita GDP gets back up to where it was before. That is not the way the National Bureau of Economic Research measures it. But I will tell you that to any-- on any common-sense definition, the average American is below where he was before, or his family, in terms of real income, GDP.James Hamilton defends the profession, conceding that it's a matter of semantics.
Economists have used the term "recession" to have this particular meaning-- the episode between a peak and trough-- for 150 years or so of data.
But it's not semantic, it's common sense. Think of a patient in a hospital. Don't we say a patient is "recovering" once the problem is identified, treated and beginning to improve? Sure, during your recovery you may still not be working or doing certain things the same as you did prior to your illness or injury, but things are moving in that direction. You're no longer getting sicker, you're getting well. In this context, the economic definition makes perfect (common) sense.