Reaction between lead dioxide and nitric acid A wikipedia article suggests that lead dioxide is produced by this reaction:
$$\ce{Pb3O4 + 4 HNO3 → PbO2 + 2 Pb(NO3)2 + 2 H2O}$$

The same article also suggests that lead dioxide reacts with nitric acid in the following way:
$$\ce{2 PbO2 + 4 HNO3 → 2 Pb(NO3)2 + 2 H2O + O2}$$

I am unable to understand why then, in the first reaction, $\ce{PbO2}$ doesn't further react with the residual nitric acid. Is it because the quantity of the acid is regulated? Or is there some error in the reactions?
You need to consider the reaction conditions.  

The Wikipedia Lead Dioxide article is saying that in dilute nitric acid the first reaction occurs, while in warm nitric acid the second reaction occurs.  

So the first reaction would only proceed to the second reaction under harsher conditions, heat and more concentrated acid.