I'm confused!
Surely you mean it's not flowing any more fuel hence the enrichment? (we are not adding air, but fuel!)
Or do you mean the flap is fully open, and so the metering head is not registering any more air flow and so not fuelling any more for it? Hence reached it's air flow limit?
Obviously this is not the physical limit of air flow through the metering head because we know it can flow more air than what it can fuel for, or the 5th injector would be pointless!