The linked paper was for strawberry juice rather than orange juice, but found that the juice lost roughly 10% of its vitamin C per hour at room temperature. They also concluded that refrigeration and the addition of sugar slowed the rate at which vitamin C was degraded.
The idea that there is a sudden plunge in concentration in the first half hour is interesting. The researchers found that the degradation reaction was zero order with respect to concentration. What that means is that no matter what concentration of vitamin C is in the juice, it will be degraded at the same rate. Reactions usually start rapidly and then slow down as the concentration of reactants decreases, but that does not seem to be the case here.
It seems perhaps your real motive is to establish the comparative health benefits. I would suggest that the healthiest option is not to juice the oranges, especially not if the pulp is filtered out. The pulp contains fibre that reduces the rate at which fructose is absorbed into the liver, which is good for the liver.
In conclusion, I'm not convinced there would be a sudden plunge in vitamin C concentration, but it is true that it undergoes fairly continuous degradation, so in terms of vitamin C intake, drinking the juice sooner will slightly up your intake. Although this is based on strawberry juice findings, which may not be generalisable to other fruits.
http://www.sciencedirect.com/science/article/pii/S1876619614000096