The stability region of the dynamic lot size problem understood as the set of cost parameter inputs for which an optimal solution remains valid has been studied in various papers of Vörös and the author. Recently van Hoesel and Wagelmans discussed these results and suggested some numerical improvement. Vörös provided explicity expressions for the boundaries of the cone-like regions. Now it will be studied how the stability region behaves if the time horizon is growing. The stability region will be shown to be non-monotonous, i.e. it may be shrinking, extending or shifting. At the same time there is some monotony connected with the planning horizon property of the dynamic lot size model, i.e. some monotonous behavior can be found for neighbor planning intervals.