There are two potential reasons:
1.) There might be a mistake in your implementation of the counterfactual simulation (bugs are an unfortunate part of computational work)
2.) When using smoothed shocks, you are considering a particular sample. Theoretical moments refer to a feature that happens when you let the simulation run for a really long time. In a particular sample, there is always some probability of getting a different result.
Did you try whether the results are consistent when you simulate the model with a longer series of shocks just drawn from their stochastic distribution, i.e. the normal distribution of the AR1-process shock? That would help exclude whether the implementation is wrong.