Formation of peracetic acid from acetic acid and hydrogen peroxide and its stability in their presence
The formation of peracetic acid from acetic acid and hydrogen peroxide is an equilibrium reaction and so in order for the peracetic acid to remain at a constant concentration as desired, acetic acid and hydrogen peroxide must also be present so that the reaction can be at equilibrium. $$\ce{CH3COOH + H2O2 &lt;=&gt; CH3COOOH + H2O}$$


  what exactly keeps the excess hydrogen peroxide from reacting with the excess acetic acid to simply form more peracetic acid?


Nothing. The hydrogen peroxide reacts with the acetic acid to form peracetic acid and water but the peracetic acid and water also react to reform hydrogen peroxide and acetic acid. At equilibrium the rates of these reactions are equal and so the concentrations of the species do not change. At room temperature the equilibrium constant is somewhere around 2.5 (see references) which indicates that significant amounts of reactants and products are present, supporting the reasoning above.

The paper Chin J Proc Eng 2008 February, 8 (1), 35–41 has some data on the values of the equilibrium constant and the variation in concentration of peracetic acid formed.

Another value for the equilibrium constant on page vii of Unis, Melod (2010) Peroxide reactions of environmental relevance in aqueous
solution. Doctoral thesis, Northumbria University.