This work investigates the interaction between a fluid solver with a CNN-based Poisson solver for unsteady incompressible flow simulations. During training, the network prediction is used to continue in time the computation, embedding the influence of the network prediction on the simulation using a long-term loss. This study investigates three implementations of such a loss, as well as the number of look-ahead iterations. On all test cases, results show that long-term losses are always beneficial. Interestingly, a partial implementation without differentiable solver is found accurate, robust and less costly than full implementation.