This work investigates the performance and limitations of the delta approximation method for parameter estimation in stochastic differential equation (SDE) mixed models. Specifically, using for illustration SDE growth models, we analyze the sensitivity of the method to the shape of the random effect distributions and explore a natural strategy to improve its performance through a reparameterization of the model. The transformation is applied to the growth coefficient parameter when it is assumed to follow a lognormal distribution, in order to evaluate if the reparameterization can lead to improved estimation accuracy. Performance comparisons between the original delta method and its reparameterization are performed using simulated datasets based on mixed SDE models inspired by real cattle weight data. The methodology is broadly applicable to other contexts that involve random-effects SDEs.