The last few pints of a keg can be bad. Some of my kegs have exhibited this, some haven't. I have no good explanation as to why some would and some wouldn't.
Oxidation shouldn't be coming into effect since you've had it on CO2 the whole time.
You could be getting yeast/trub/other settlers getting kicked up, but with a keg that's been sitting you'd need to jostle it to do that.
I could see it being a beer that doesn't age well, but in my experience you don't see a sudden degredation in flavor like you're describing. This is an interesting problem you've got.