In this case I'd say the oil is reaching the end of it's useful life but not quite yet.
"One other thing... Most folks would consider an engine oil to be shot when the TBN reaches 2 - 3. This isn't actually the case. An oil can function quite happily with a TBN of zero. The thing you have to remember is that oil formulators don't tend to focus directly on stuff like TBN depletion, acid formation or oil oxidation. What they're really concerned with is the onset of exponential viscosity increase. For many of the lengthy, industry standard engine based oxidation tests, it's both impractical and uneconomic to just use over based detergent to control oxidation. Given how fast it can deplete, you might need an oil with a starting TBN of around 20 to keep the TBN above 2 at the end of the test! For this reason, modern oils contain a cocktail of various Antioxidant chemistries, each of which plays a role in keeping the oil from 'breaking' long after the TBN reserve has been exhausted. Just to be clear, there's nothing wrong per se with changing out your oil when the TBN hits 2 - 3 but if you do a UOA, and find the oil's TBN is zero, it's not something to freak out about."