That would explain only a slowing in the rate of wealth increase, not a decrease in wealth.
Unfortunately, we also tend to be habit creatures, and our burn rate often stabilizes to our pay and our social class (keeping up with the Jones'). If our real wage starts to go down, then we often have trouble adapting, and keep burning as if we were still at the prior equilibrium (credit card debt, eating into savings, taking out loans).
This is made even worse when the source of real wage reduction is the subtle erosion of our buying power through inflation. We complain about how much things cost, but we still see our paychecks slightly increasing so it seems good, and the burn gets worse.