Realistically you only take about 2% Oxygen with each breath even though the air is anywhere from 20-30% Oxygen, I don't see why having Oxyrush nanites which can grab the extra 18-28% Oxygen in a single breath degrade in such a fast amount of time. Once the Oxygen is spent it can easily grab more from your lungs unlike your two examples O-Cell and Nantidotes. Nantidotes are loaded up with highly specific chemicals that take weeks to replenish using your own bodies chemicals, and O-Cell nanites imitate O-cells which actively die to 'fighting' diseases.
From a realism standpoint, this makes good sense.
It takes roughly one minute for blood to fully circulate. If the Oxyrush is so much better than hemoglobin at grabbing and holding oxygen, then it shouldn't take long at all for it to recharge its payload.
From a game-balance standpoint, the internal airtank refills 2 hours of oxygen in 5 minutes without any specialized machinery. So, the cyber alternative is already bonkers.
So, unless the GM wants to make a big deal of it (plot wise,) I'd not worry about how long it takes Oxyrush to refill.
As to degradation, if it doesn't say that use degrades it, then there's no reason to think that it does.